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Physics Laboratory Manual Equipotential and Electric Field Lines
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Equipotential and Electric Field Lines
Student’s Guide
Laboratory Manual
(2017)
Physics Laboratory Manual Equipotential and Electric Field Lines
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PACKING LIST
1. Black Conductive Paper
2. DC Power Supply
3. Multimeter (Voltmeter)
4. Graph Paper
5. Corkboard
6. Pushpins
7. Connecting Wires
8. Standard Power Cable
9. Student and Teacher Manuals
Physics Laboratory Manual Equipotential and Electric Field Lines
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Contents
1. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. Electric Potential and Potential Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4. Electric Potential Due to Point Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5. Relation between Electric Potential and Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6. Equipotential Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7. Electric Fields and Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
8. Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9. Laboratory Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Physics Laboratory Manual Equipotential and Electric Field Lines
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The objectives of this laboratory experiment are;
1) To study the relation between the equipotential
lines and electric field,
2) To investigate and map the equipotential lines of
two oppositely charged conductors,
3) To plot the electric field lines using the
equipotential lines in two dimensions,
4) To study the effect of a conducting ring on the
equipotential and electric field lines.
An electric charge exerts a force of attraction or
repulsion on other electric charges. The force a
charged object exerts on a second one is proportional
to the product of the magnitude of the charge on one
( ) times the magnitude of the charge on the other
( ), and inversely proportional to the square of the
distance between them. As an equation, we can
write the electrostatic force between any two charges
as;
(1)
This is the Coulomb’s law. In this expression is
proportionality constant. Coulomb’s law, Equation-(1),
gives the magnitude of the electric force that either
charge exerts on the other. Keep in mind that
Equation-(1) represents the force on a charge due to
only one other charge, a distance apart. The
direction of the electric force is always along the line
joining the two charges. If the two charges have the
same sign, the force on either charge is directed away
from the other (that is, they repel each other). However,
if the two charges have opposite signs, the force on
one is directed toward the other (they attract).
Figure-1: Work is done by the electric field in moving the
positive test charge from the position to the position
. Electric field lines are parallel and equally spaced in
the central region.
The constant is often written in terms of another
constant called the permittivity of free space. It is
related to by ⁄ . So, the electrostatic force
can be rewritten as;
(2)
where,
We can define the potential energy for the
electrostatic force. Consider the electric field
between two equally but oppositely charged parallel
plates (Figure-1). Also consider a positive point charge
placed at point a very near the positive plate. If this
charge at point is released, the electric force will
do work on the charge and accelerate it toward the
negative plate.
1. Purpose
2. Electric Potential and Potential Difference
Physics Laboratory Manual Equipotential and Electric Field Lines
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The work done by the electric field to move the
charge a distance is given by;
(3)
where we used the relation, .
The change in electric potential energy equals the
negative of the work done by the electric force;
(4)
This means that the potential decreases (that is, is
negative). As the charged particle accelerates from
point to point , the particle’s kinetic energy
increases. According to the conservation of energy,
electric potential energy is transformed into kinetic
energy and so the total energy is conserved. The
positive charge has its greatest potential energy at
point , near the positive plate. For a negative
charge, its potential energy is greatest near the
negative plate.
Now, it is useful to define the electric potential (or
simply the potential, ) as the electric potential energy
per unit charge. If a positive test charge in an
electric field has electric potential energy at some
point (relative to zero potential energy), the electric
potential at this point is;
From this expression, we can write as;
(6)
Potential is potential energy per unit charge. We
define the potential at any point in an elelctric field as
the potential energy per unit charge associated with
a test charge at that point. Potential energy and
charge are both scalar, so potential is a scalar
quantity.
The potential difference between two points and
(in the case of Figure-1, between and ) is
measurable and given by;
or,
We call and the potential at point and
potential at point , respectively. Thus, the work
done per unit charge by the electric force, when a
charged particle moves from to , is equal to the
potential at minus potential at . Note that the
difference is called the potential of with
respect to . The field is directed from regions of
high potential to regions of low potential. The
magnitude of the electric field is largest in region
where is large. Conversely, the electric field is
zero in regions where is constant. In electric circuits,
the unit of electric potential (and potential difference) is
given by ⁄ or . Potential difference
(since it is measured in volts) is often referred to as
(note that ⁄ ).
(5)
(7)
(8)
Physics Laboratory Manual Equipotential and Electric Field Lines
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3. Electric Field
The electric field at any point in space is defined as
the force exerted on a positive test charge placed at
that point divided by the magnitude of test charge ;
(9)
Here, is the electrostatic force (or Coulomb force)
exerted on a positive test charge, . It is important to
recall that is in the same direction as . It is assumed
that is so small that it does not change the charge
distribution creating the electric field. The test charge
is so tiny that it exerts no force on the other charges
which created the field. For simple situations involving
a single point charge (a particle having a charge, ),
we can calculate the field . The field at a distance
from the point charge has a magnitude;
(11)
Since is a vector quantity, it should have a direction
as well as a magnitude. The direction of the electric
field produced by any charge distribution is the
direction of the force acting on a test positive charge
placed in the field. As you see from the expression, the
electric field is completely independent of the test
charge, . Note that the field depends only on the
charge which produces the field. If we are given
the electric field at a given point in space, then we
can calculate the force on any charge placed at
that point by writing;
(13)
The electric field lines for a point charge are shown
in the Figure-(2). Here, only a few representative lines
are shown. For a single positive point charge, the lines
point radially outward from the charge (Figure-2a) and
for a negative point charge, they point radially inward
toward the charge (Figure-2b). Their density (that is,
their closeness in any region is proportional to the
intensity of the field in that region). Note that nearer the
charge, where the electric field is greater, the electric
field lines are closer together. This is an important
property of electric field lines. Since the electric field
can have one and only one direction at any point in
space, no two electric field lines can pass through the
same point. That is, the electric field lines do not
intersect.
⁄
(10)
(Single Point Charge) (12)
(a)
(b)
Figure-2: Electric field lines of a single positive point charge
(a) and the lines of a single negative point charge (b). The
electric field is stronger where the field lines are closer
together.
Physics Laboratory Manual Equipotential and Electric Field Lines
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The electric potential at a distance from a single
point charge can be derived directly from the
equation;
∫ (14)
The field is directed radially outward from a positive
charge (inward if ). Figure-(3) shows some of the
electric field lines in a plane containing a single positive
charge. We can take the integral along a straight field
line from point (a distance from ) to a point
(a distance from ). Then, will be parallel to
and . So;
∫
(15)
The electric field due to a single point charge has a
magnitude;
or,
where
⁄ .
Using this expression, we get;
If we choose the potential to be zero at infinity1 (that is,
let at ), then the electric potential at a
distance from a single point charge will be;
This expression for potential implies that is a
constant if is constant. Therefore, equipotential
surfaces (that is, a surface with a constant value of
potential at all points on the surface) of a single point
charge are concentric spherical surfaces centered at
the charge. The potential near a positive charge is
large and it decreases toward zero at very large
distances. However, for a negative charge the
potential is negative and increases toward zero at large
distances. We will deal with the concept of
equipotential surfaces later.
1 Note that we let point be at distance and point
be at infinity. Then, we choose the potential to be zero at infinite distance from the charge.
4. Electric Potential Due to Point Charges
Figure-3: Calculating the electric potential by integrating
for a single point charge.
(16)
(17)
∫
(18)
(
) (19)
(
) (20)
[
] (21)
Physics Laboratory Manual Equipotential and Electric Field Lines
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5. Relation between Electric Potential and
Electric Field
The difference in potential energy between any two
points in space and is given by;
∫
(22)
This is the relation between a conservative force and
the potential energy associated with that force. Here,
is an infinitesimal increment of displacement. So,
the integral is taken along any path in space from point
to point . Remember that a conservative force is
one for which the work done by the force on a moving
object from one position to another depends only the
two positions and not on the path taken. For example,
the force of gravity is a conservative force. For the
electrical case, we are interested in the potential
difference;
⁄ (23)
As mentioned previously, the electric field at any
point in space is defined to be the ratio of the Coulomb
force to the test charge;
where is the electrostatic force (or Coulomb force)
exerted on a positive test charge . In defining the
electric field, we specify that the test charge is so
small that it does not alter the charge distribution
creating the electric field.
Solving for from these expressions gives;
(25)
∫
(26)
∫
(27)
This is the general relation between electric field, and
potential difference, . In the Figure-(1), for example,
a path parallel to electric field lines from point at
the positive plate to point at the negative plate gives
us;
∫
(29)
Since and are in the same direction at each point,
we can write the potential difference as;
∫
(30)
(31)
Here, is distance parallel to the field lines between
points and . Note that this equation is true only if
the electric field is uniform. The units for electric field
intensity can be written as volts per meter ( ⁄ ) as
well as per Coulomb ( ).
An electric field line is an imaginary line or curve
drawn through a region of space. The direction of the
electric field at any point is tangent to the field line
through that point. Electric field lines show the
direction of at each point and their spacing gives an
idea of the magnitude of the electric field . Where the
electric field is strong, we draw field lines bunched
closely together. Conversely, where is weaker, they
are farther apart. It is also useful to know that two field
lines never intersect one another (that is, only one
field line can pass through each point of the field.). If
they did, the intersection would be a point at which
electric field has two directions. That is to say; the
force on a test charge would have two directions!.
(24)
∫
(28)
Physics Laboratory Manual Equipotential and Electric Field Lines
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Figure-4: Electric field generated between two oppositely
charged parallel plates.
Consider a system of two metal plates with opposite
charges on them, as shown in the Figure-(4). In
electrostatic equilibrium, the electric field between
the plates (conductors) will be uniform in strength and
direction, except near the edges. The excess charges
distribute themselves uniformly, producing field lines
that are uniformly spaced and perpendicular to the
surfaces. The plates are charged to produce a
potential difference of . The separation between the
plates is . With this information, we can
determine the magnitude of the uniform electric field in
the space between the plates.
⁄
To calculate the magnitude of , assumed uniform, we
apply ⁄ . From this, the electric field magnitude
is ⁄ ⁄ .
Physics Laboratory Manual Equipotential and Electric Field Lines
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As explained, electric potential is described as
electric potential energy per unit charge. The electric
potential difference between any two points in space is
defined as the difference in potential energy of a test
charge placed at those two points, divided by the
charge, . That is, ⁄ . The electric
potential can be represented graphically by drawing
equipotential lines, or in three dimensions,
equipotential surfaces2. Remind that an equipotential
surface is one on which all points are at the same
potential. This means that the potential difference
between any two points on the surface must be
zero (that is, ).
2 An equipotential line or surface is all at the same
potential and is perpendicular to the electric field at all points.
The equipotential surface is always perpendicular to
the electric field at any point. On a surface where is
constant such that , so we must have either
, in the expression ∫ or,
where is the angle between and
vectors. Therefore, in a region where is not zero, the
path along an equipotential must have ,
meaning and the field is perpendicular to
the equipotential.
Equipotential surfaces (also called equipotential lines
in two-dimensional drawings) are a very useful method
to visualize the electric field and how it varies in
space. Equipotential surfaces are always perpendicular
to the direction of the electric field. In other words,
electric field lines and equipotential surfaces are
mutually perpendicular. This property follows from the
relationship between and . This fact helps us locate
the equipotential surfaces (equipotential lines) and
field lines for a graphical representation. It is
obvious that all points having the same potential will
define an equipotential surface. Also you know that
electric field lines and equipotential surfaces are
always perpendicular. Thus, an imaginary filed line can
be constructed through each of the successive
equipotential surfaces while maintaining the
perpendicularity. This will define a field line through
the electric field.
A basic geometry for the visualization of an electric
field (a field line) is that of a parallel plate capacitor
(see Figure-5). It has two parallel plates each carrying
an equal and opposite electrostatic charge. Between
the plates there will be an electric field (that is, a region
in space where electric forces are experienced). The
equipotential surfaces are parallel planes with
perpendicular field lines. As the example of a parallel
plate capacitor, a few of the equipotential lines are
drawn (dashed lines) for the electric field lines between
two parallel plates at a potential difference of . The
negative plate is chosen to be zero volts and the
potential of each equipotential line is indicated.
6. Equipotential Surfaces
Figure-5: Equipotential lines (dashed lines) between two
oppositely charged parallel metal plates. The equipotential
lines (planes parallel to the metal plates) are perpendicular to
the electric field lines. Note that points toward lower
values of .
Physics Laboratory Manual Equipotential and Electric Field Lines
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By definition, the electric field of a point charge always
points away from a positive charge but toward a
negative charge. To visualize the electric field, we draw
a series of lines to indicate the direction of the electric
field at various points in space. These electric field
lines are sometimes called lines of force3. They are
drawn so that they indicate the direction of the force
due to the given field on a positive test charge. That
is, the direction of the electric field is the direction of
the force that the test charge experiences. The electric
field can therefore be mapped graphically by lines of
force.
For a simple case of a positive charge, the electric field
lines is directed radially outward, as shown in the
Figure-(6a), because a positively charged test particle
would be repelled radially. The field lines point radially
outward from the charge. The field lines in the plane
of the charge are represented by the by straight lines
and the intersections of the equipotential surfaces
(dashed lines) with this plane (that is, cross sections of
these surfaces) are shown as dashed lines. The actual
equipotential surfaces are three-dimensional. At each
crossing of an equipotential and a field line, the two are
perpendicular since equipotential lines (dashed) are
always perpendicular to the electric field lines.
3 Electric field lines are represented by the lines of
force drawn to follow the direction of the field. These lines are always perpendicular to the equipotential surfaces.
For the case of a negative charge, the force lines
(lines of force) are radially directed inward toward the
negative charge, as a positively charged test particle
would be attracted radially (see Figure-6b).
We can draw the lines so that the number of lines
starting on a positive charge or ending on a negative
charge is proportional to the magnitude of the point
charge. Notice that nearer the point charge, where the
electric field is greater, the lines are closer together. In
other words, the closer together the lines are, the
stronger the electric field in that region.
In general;
Field lines help us visualize electric fields.
The potential at various points in an electric field
can be represented graphically by equipotential
surfaces (or, equipotential lines in two-dimensional
drawings).
Electric field lines and equipotential surfaces are
mutually perpendicular.
We can use a digital (voltmeter) and two
probes (for example, two metal rods) to measure the
potential difference between the two probes. By
placing the probes (connected to the terminals of the
voltmeter) in various positions in an electric field, we
can read the potential differences between the two
positions of the probes. Equipotential surfaces can be
determined by leaving one probe at a fixed position
and then moving the other probe. Whenever the
voltmeter reads zero, the moving probe is at the same
potential as the non-moving probe. That is, the
potential difference between the two probes is zero.
From these considerations, we can map the electric
field from the equipotential lines. On an equipotential
surface where is constant, so . This implies
that the potential remains constant along a path that
is perpendicular to the force lines. Such a path that has
the same value of potential at all points on it is called
an equipotential line in two dimensions, and an
equipotential surface in three dimensions. The field
lines are always perpendicular to the equipotential.
(a) (b)
Figure-6: Electric field lines and equipotential surfaces for a
single positive point charge (a) and a single negative point
charge (b). The field due to a positive charge points
away from the charge, whereas due to a negative charge
points toward that charge.
Physics Laboratory Manual Equipotential and Electric Field Lines
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As you know, the electric field due to a positive point
charge is visualized by straight lines originating from
the source charge and that due to negative charge by
straight lines terminating at that charge. In the case of
a positive point charge, the electric field is directed
radially outward (Figure-7). Since the equipotential
surfaces must be perpendicular to the lines of the
electric field, they will be spherical in shape, centered
on the point charge (that is, on a given equipotential
surface, the potential has the same value at every
point). Note that different spheres correspond to
different values of . However, the electric field
magnitude needs not to be same (constant) at all
points on the equipotential surface.
In regions where the magnitude of is large, the
equipotential surfaces are close together.
Conversely, in regions where the field is weaker,
the equipotential surfaces are farther apart. This
happens at larger radii, as illustrated in Figure-(7).
The equipotential surface with the largest potential is
closest to the positive charge. As an example, consider
a positive point charge . Assume that
the equipotential surfaces (or lines in a plane
containing the charge) correspond to ,
, . Now, we can sketch the
equipotential surfaces. Recall that the electric potential
depends on the distance from the charge;
From this expression, we have;
For ,
Similarly, for , we get and for
, .
As mentioned earlier, an equipotential surface is a
surface on which the potential has the same value at
every point. Electric field lines and equipotential
surfaces are always mutually perpendicular. In two
dimensional drawings, it is convenient to connect
points of equal potential with lines (these lines are
called equipotential lines).
At a point where a FIELD LINE crosses an
equipotential surface, the two are perpendicular.
For the special case of uniform electric field, in which
the field lines are straight, parallel and equally spaced,
the equipotential surfaces will be parallel planes
perpendicular to the field lines. In other words, for a
uniform electric field, the equipotential surfaces are
parallel planes at right angles to the direction of electric
field.
Figure-7: Electric field lines and equipotential surfaces for a
point charge. The equipotential surfaces around a point
charge are spheres. The circles are projections of the
spherical surfaces onto the plane of the drawing. If you
move in the direction of , electric potential decreases. If
you move in the direction opposite , increases.
[
] (32)
(
) (33)
(
) (34)
Physics Laboratory Manual Equipotential and Electric Field Lines
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In an electric field produced by a given charge
distribution, there will be many points that have the
same potential. These points are called equipotential
points. If one locates all the equipotential points and
then joins them, one gets an equipotential line. All
points lying on an equipotential line will have the same
potential. The equipotential lines of a given charge
distribution should be perpendicular to the electric field
lines.
A drawing of the electric field lines and equipotential
surfaces of two equal and opposite charges (two
unlike charges) is shown in the Figure-(8). The electric
field of two unlike charges is stronger between the
charges. In that region, the fields from each charge are
in the same direction, so their strengths add. At very
large distances, the field of two unlike charges looks
like that of a smaller single charge. The equipotential
lines are drawn by making them perpendicular to the
electric field lines, if those are known. The electric field
lines are curved in this case and are directed from the
positive charge to the negative charge. The direction
of the electric field at any point is tangent to the field
line at that point. Note that the potential is greatest near
the positive charge and least near the negative charge.
Conversely, if the equipotential lines are known, the
electric field lines can be drawn by making them
perpendicular to the equipotential lines.
Figure-(9) shows the electric field lines for two equal
positive charges. The electric field is weaker between
two same charges, as shown by the lines being farther
apart in that region. This is because the fields from
each charge exert opposing forces on any charge
placed between them. At a great distance from two
same charges, the field becomes identical to the field
from a single, larger charge.
The field lines provide a graphical representation of
the electric fields. So, we can use electric field lines to
visualize and analyze electric fields. At any point on a
field line, the tangent to the line is in the direction of
at that point. In conclusion, it can be said that the
potential at various points in an electric field can be
represented graphically by equipotential surfaces (in
two-dimensions the equipotential surfaces are
equipotential lines);
Graphical representations can be constructed by
drawing equipotential surfaces and field lines.
An equipotential surface is everywhere
perpendicular to the electric field lines (lines of
force) that intersect it. However, electric field lines
never intersect one another. This fact allows us to
use the equipotential surfaces to sketch the
electric field lines.
(a)
Figure-8: Electric field lines due to two equal charges of
opposite sign. Equipotential lines (dashed lines) are always
perpendicular to the electric field lines for two equal but
oppositely charged particles.
Figure-9: Electric field lines and equipotential lines of two
positive equal (same) charges. Lines of force (electric field
lines) are shown as solid lines and arrows. Equipotential
lines are shown as dashed lines.
Physics Laboratory Manual Equipotential and Electric Field Lines
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In this chapter, we will discuss some properties of
conductors. Conductors contain free charges that
move easily. When there is no net motion of charge
within a conductor, the conductor is said to be in
electrostatic equilibrium. The electric field is zero
everywhere inside the conductor, whether it is solid or
hollow. If the field were not zero, free electrons in the
conductor would experience an electric force ( )
and would accelerate due to this force. This motion of
electrons would mean the conductor is not in
electrostatic equilibrium. Thus, the existence of
electrostatic equilibrium is consistent only with zero
field in the conductor.
We can investigate how this zero field is achieved. Let
us consider a conductor in the form of a slab, as shown
in the Figure-(10). Just before the external field is
applied, free electrons are uniformly distributed
throughout the conductor. When an external field is
applied, the free electrons accelerate, causing negative
charge to accumulate on one side (left surface). The
movement of electrons to one side results in a plane of
positive charge distribution on the right surface.
For a thin flat conductor, the charge accumulates on
the outer surfaces only. These surfaces (planes) of
charge create an additional electric field inside the
conductor that opposes the applied external field. As
the electrons move, the surface charge densities on the
left and right surfaces increase until the magnitude of
the internal field equals that of the external electric
field. This process results in a net field of zero inside
the conductor.
The field must be perpendicular to the conductor’s
surface from the condition of the electrostatic
equilibrium. If the field vector had a component
parallel to the conductor's surface, free electrons would
experience an electric force and move along the
surface. In such a situation, the conductor would not be
in equilibrium. Thus, the electric field at a point just
outside a charged conductor is perpendicular to the
surface (that is, the electric field vector must be
perpendicular to the surface).
7. Electric Fields and Conductors
Figure-10: A slab conductor in an external electric field. The
induced charges on the two surfaces of the conductor
produce an electric field that opposes the external field,
giving a net (resultant) field of zero inside the slab.
Physics Laboratory Manual Equipotential and Electric Field Lines
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Now, suppose that a positive charge is surrounded
by an isolated uncharged metal conductor whose
shape is a spherical shell (see Figure-11). There can
be no field within the metal, so the lines leaving the
central positive charge must end on negative charges
on the inner surface of the metal. Thus an equal
amount of negative charge ( ) will be induced on the
inner surface of the spherical shell.
Since the shell is neutral, a positive charge of the same
magnitude ( ) must exist on the outer surface of the
shell. Therefore, although no field exists in the metal
itself, an electric field exists outside of it. There can be
no electric field within a conductor in the static case, for
otherwise the free electrons would feel a force and so
would move. In fact, the entire volume of a conductor
must be entirely at the same potential in the static
case, and the surface of a conductor is then an
equipotential surface4. We know that the field
everywhere inside the conductor, otherwise, charges
would move. It flows that at any point just inside the
surface the component of tangent to the surface is
zero.
4 The surface of a conductor is an equipotential
surface and electric field lines are always normal to the surface.
Some properties of a conductor in electrostatic
equilibrium can be summarized as follows;
1. The electric field is zero inside a conductor.
2. Just outside a conductor, the electric field lines are
perpendicular to its surface, ending or beginning on
charges on the surface.
3. Any excess charge resides entirely on the surface
of a conductor that is, if a conductor in equilibrium
carries a net charge, the charge resides on the
conductor's outer surface. Outside the conductor,
the field is exactly the same as if the conductor
were replaced by a point charge at its center equal
to the excess charge.
4. In the static situation that is, when the charges
are at rest, the surface of any charged conductor is
always an equipotential surface; the electric
potential is constant inside the conductor and is
equal to the potential at the surface of the
conductor.
Figure-11: A charge inside a neutral spherical metal
conductor (shell) induces charge on its surface. Induced
charges appear on the inner and outer surfaces of the
conductor. The electric field within the conductor itself is
zero.
Physics Laboratory Manual Equipotential and Electric Field Lines
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An uncharged (neutral) conductor placed in a uniform
electric field is polarized with the most concentrated
charge at its most pointed end. Free charges move
w ithin the conductor, polarizing it , unt il the electric
f ield lines are perpendicular to the surface (that is,
the f ield lines bend so that the external f ield at the
surface is alw ays perpendicular). The external
electric f ield lines end on excess negative charge on
one sect ion of the surface and begin again on
excess posit ive charge on the opposite side. No
electric field exists inside the conductor in static
equilibrium with the external uniform electric field. That
is, in the electrostatic situation, the electric field in the
conductors will be zero, and therefore, all points in on
the conductors will be at the same potential .
Consider a uniform electric field pointing in the positive
direction (Figure-12a). When a neutral conductor of
arbitrary shape is inserted into the external electric field
(Figure-12b), the electric field is distorted and charge
separation occurs on the surface of the conductive
object. Being an equipotential surface, the object
(conductor) is at the potential of the electric field even
though there is no net charge on the surface. Under
electrostatic conditions, the electric f ield inside the
conductor must be zero. No electric f ield exists
inside the conductor.
We can map electric field lines by determining
equipotential lines of two oppositely charged
conductors. Having plotted sufficient equipotential lines
we may then map out the electric field lines which are
normal (perpendicular) everywhere to them. To map
the equipotential lines in a medium between a pair of
charged electrodes and to draw the electric field lines
perpendicular to these lines, the method involves
measuring the potential difference between every two
points in the conductivity medium surrounding two
charged conducting electrodes. The carbon paper
forms the conducting medium or space between the
electrodes. Using a voltmeter, you can measure the
potential difference between any two points in the
medium. If there is no potential difference between any
two points, they must be at the same potential and thus
lie on the same equipotential line.
An equipotential line is a line along which the
electric potential is constant (same). That is, the
potential difference between any two points on an
equipotential line is zero.
Equipotential lines are always perpendicular to
electric field lines. This concept can be used to
draw electric field lines around any type of charge
distribution if the equipotential lines are first
determined. The detailed experimental procedures
are given in the next section.
(a) (b)
Figure-12: A uniform electric field before an uncharged conductor is placed in the field (a). Afterward, the electric field is changed
dramatically, with no electric field inside the conductor (b). Induced charges, which make the electric field inside the conductor
zero, appear on the outside surface of the conductor. There charges affect the electric field outside the conductor.
Physics Laboratory Manual Equipotential and Electric Field Lines
17
1. Plan and draw the layout of two conductive
rings (charged paths) on a graph paper.
1.1. Since these charged paths (charge distributions)
can be any two dimensional shape, such as
circles or dots, they will be referred to as
conductive ink electrodes.
1.2. Draw the rings (two sets of electrodes)
symmetrically along the -axis and -axis on the
paper.
2. Mount the conductive paper (carbon paper) on
the corkboard by using one of the metal pushpins
in each corner of the paper.
Figure-14: Connection of the pin, electrode, wire and
paper on the corkboard.
3. Set up the circuit shown in the Figure-(13).
3.1. Connect the electrodes (two ink electrodes on
the carbon paper) to a power supply by using
connecting wires. Remember that the electrodes
on the carbon paper can be any two-dimensional
shape, such as dots, straight lines or circles.
3.2. Place the terminal of the connecting wire over the
conducting ring electrode and then stick a push
pin through its terminal and the electrode into the
corkboard (see Figure-14).
3.3. The push pin does not act as a conductor. Its
function is only to hold the connecting wire against
the electrode.
8. Experimental Procedures
In this study you will determine and map some of the equipotential lines of a system of oppositely charged conducting rings. The
conducting rings are connected to a power supply. They are drawn by silver conductive ink pen on a black conductive paper
placed on a hard surface. The potential difference between any two points can be measured by touching the probes to the paper at
those points. If two points are at the same potential then these points are called equipotential points.
Figure-13: Experimental circuit for the determination of the
equipotential lines of a system. The conducting rings are
connected to a DC power supply.
To connect wires to the ink electrodes, clean the
terminal on a wire; attach it on an electrode, then
stick a metal push pin through both the terminal
and the electrode into the corkboard. Be sure the
terminal on a wire makes good electrical contact
with the electrode.
Physics Laboratory Manual Equipotential and Electric Field Lines
18
4. Now, check the rings (electrodes) for proper
conductivity. For this procedure;
4.1. Connect one voltmeter probe to a conducting
ring (electrode) near its pushpin.
4.2. Touch the voltmeter’s second probe to several
other points on the same electrode.
4.3. If the ring has been properly drawn, the maximum
potential difference between any two points on the
same electrode will not exceed 1% of the potential
difference between the two electrodes (that is, the
applied power supply voltage).
5. A two-dimensional electric field will be produced
when a voltage is applied across two metal
electrodes that touch the conductive paper.
5.1. Adjust the output voltage of the power supply to
5-6 volts and switch on.
5.2. It is important to keep in mind that if the ground
terminal of the voltmeter is connected to the
negative electrode, and the positive probe to the
other, the volt meter will read the voltage
applied by the power supply.
5.3. To plot the equipotential lines, the ground probe
(one lead) of the voltmeter is touched to the
negative electrode. The potential of this electrode
will be your zero reference potential.
5.4. The second voltmeter probe is touched to any
point on the carbon paper to measure the
potential at that point with respect to the ground
electrode.
6. Now, you are ready to choose six reference
points along the -axis of the paper ( , , , ,
and ).
6.1. Choose these points to be distributed
symmetrically about the origin.
6.2. Touch the probe to one of these points and then
measure and record the potential of this point
with respect to the reference electrode.
. . . . .
6.3. To map an equipotential, move the probe until
the same potential is indicated on the voltmeter.
6.4. Mark the paper at this point with a soft lead
pencil.
6.5. Continue to move the probe, but only in a
direction which maintains the voltmeter at the
same reading. That is;
. . . . .
6.6. Find such ten equipotential points, five above
and five below the -axis.
6.7. Repeat the experiment for the six reference
points you had already chosen on the paper.
6.8. Draw your points on a graph paper representing
the carbon paper.
7. Draw the equipotential (constant voltage) lines
by connecting the equipotential points for each
reference point by a smooth curve.
8. Using the fact that the electric field lines are
perpendicular to the equipotential lines, draw the
electric field lines in the region between two
charged rings.
Recall that electric field lines can never cross.
Field lines must begin on positive charges and
terminate on negative charges for any charge
distribution.
8.1. What are the directions of the electric field lines
for the experimental configuration of two equal
and opposite charge distributions?.
8.2. Are the field lines close together at places where
the field magnitude is large?.
Physics Laboratory Manual Equipotential and Electric Field Lines
19
9. Define equipotential line. How are electric field
lines and equipotential lines drawn relative to
each other?.
10. Will the electric field always be zero at any point
where the electric potential is zero?. Why or
why not?.
11. Will the electric potential always be zero at any
point where the electric field is zero?.
12. By using the carbon paper which already has a
ring, for three of reference points ( , , and ),
investigate the equipotential points in the quarter
in which the ring lies.
12.1. By finding these new equipotential points,
draw the equipotential lines and electric field
lines near the conducting ring on a second
graph paper.
Note that equipotential lines are lines
joining points of the same electric
potential. All electric field lines cross all
equipotential lines perpendicularly.
12.2. How do the equipotential (constant voltage)
lines vary in the presence of the conducting
ring?.
12.3. Draw also the new electric field lines.
Remember that the electric field is zero
inside a conductor. Just outside a
conductor, the electric field lines are
perpendicular to its surface, ending or
beginning on charges on the surface.
12.4. What is true about the electric field just outside
the surface of a conductor?.
12.5. Using the voltmeter probes, verify that the
surface of the conducting ring is indeed an
equipotential surface.
Physics Laboratory Manual Equipotential and Electric Field Lines
20
1. By finding the equipotential points and lines, draw
the electric field lines of two charged rings on the
graph paper. How did you find the direction of the
electric field lines on your graph?.
2. Draw the equipotential lines and electric field lines
near the conducting ring on a second graph
paper.
3. What was the effect of placing the ring on the
equipotential lines and the electric field lines.
4. Describe briefly how you verified that the surface of
the conducting ring is an equipotential surface.
5. Why do we need equipotential lines to draw electric
field lines?.
6. Can two or more equipotential lines intersect each
other?. Explain, briefly.
7. What would happen to the equipotential lines and to
electric field lines when the terminals are reversed?.
9. Laboratory Report
Name: __________________________________
Department: __________________________________
Student No: __________________________________
Date: __________________________________
Physics Laboratory Manual Equipotential and Electric Field Lines
21
Graph-1: Equipotential curves and electric field lines drawn on the graph paper.
Physics Laboratory Manual Equipotential and Electric Field Lines
22
Graph-2: Equipotential lines and electric field lines near the conducting ring on the second graph paper.