PAL #11 Electric Field
Electric field between charge +3q and charge -1q
Ratio of lines touching 3q to lines touching -1q must be 3 to 1
At large distance away acts as net
charge of +2q
PAL #11 Electric Field To find electric field at a point between the charges:
E = “q” for the charges is e = 1.6X10-19 C,
3q = (3)(1.6X10-19) = 4.8X10-19 C 1q = (1)(1.6X10-19) = 1.6X10-19 C
Find E from the 3q charge, find E from the 1q
charge Since both fields point the same way (to the right), add
them up
The above electric field,
A) increases to the rightB) increases to the leftC) increases upD) increases down E) is uniform
Is it possible to have a zero electric field on a line connecting two positive charges?
A) Yes, at one point on the lineB) Yes, along the entire lineC) No, the electric field must always be
greater than zeroD) No, but it would be possible for two
negative chargesE) No, the electric field is only zero at
large distances
A hollow block of metal is placed in a uniform electric field pointing straight up. What is true about the field inside the block and the charge on its top surface?
A) Field inside points up, charge on top is positive
B) Field inside points down, charge on top is negative
C) Field inside points up, charge on top is zero
D) Field inside is zero, charge on top is positive
E) Field inside is zero, charge on top is zero
Electrical Force and Energy Like any other force, the electrical force
can do work:
If a force does work, the potential energy must decrease e.g.
Decrease in PE (PE) equal to the workPE = -W = -qEd
We would like to define a quantity that
tells us about the electrical energy at a point in the field that does not depend on the test charge
Potential Difference The potential difference (V) between
two points is the difference in electrical potential energy between the two points per unit charge:
V = Vf - Vi = PE/q
For any given point with potential V Potential is the potential energy per unit
charge Potential given in volts (joules/coulomb)
1V = 1 J/C
Potential Confusion
The potential and the potential energy are two different things
Potential at a point is the same no mater what kind of test charge is put there
e.g. V = 12 V (potential is equal to 12 volts)
Signs As a positive charge moves along the electric field,
the particle gains kinetic energy and the field loses potential and potential energy
The potential energy lost by the field goes into work Since energy must be conserved:
An electric field will naturally move a positive
particle along the field lines, doing positive work and resulting in a decrease in potential and potential energy n.b.
E+
Down field does work “
Up gain PE
field “does” negative work
For negative
particle, everything is backwards
Work We will talk of work done by the system and
work done on the system Work done by the system is positive if
it decreases the potential energy
Work done by the system is negative if it increases the potential energy
The negative work done by the system is the positive work done on the system
Today’s PAL Consider 4 situations: + charge moves with E
field, + charge moves against E field, - charge moves with E field, - charge moves against E field
For each situation: What is the sign of the change in potential energy? What is the sign of the potential difference (final-
initial)? What is the sign of the work done by the system? Does this happen naturally?
Work and Potential
Positive work done by the electric force reduces potential energy (W = -PE)
We can also write work as
If there is no potential difference there is no work done by the electric force
Potential and Energy We can convert potential energy into kinetic
energy As a particle moves from an initial to a final
position, energy is conserved:
Since PE = Vq KEf = KEi + qVi -q Vf
Thus if you go from high to low potential (“downhill”) the particle speeds up
Conductors
All points on the surface must be at the same potential
Since there is no field inside the conductor, the electric potential is constant inside the conductor
Equipotentials Equipotentials lines are drawn perpendicular to
the electric field
The equipotentials for a single point charge are a series of concentric circles
Equipotentials cannot cross This would mean the same point had two values for V
Point Charges and Potential
Consider a point charge q, what is the potential for the area around it? At infinity the potential is zero
It can be shown that:V = ke q / r
For a single point charge
Potential Energy and Two Charges
Since the potential energy is just qV, for two point charges:
The electrical energy of the situation
depends on how far apart they are and their charge Example: two positive charges brought
close together have an increase in potential energy
Finding Potential
Potential is a scalar (not a vector) and so can be found by summing the magnitudes of the potentials from each charge Total V = V1 + V2 + V3 …
Top Related