1-2 Electric Fields

8/19/2019 1-2 Electric Fields

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PhysicsLinX TM Review LecturesPrinciples of Physics II

by

Martin O. OkaforAssociate Professor of Physics


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PP2.1: Electrostatics


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1-2: Electric Field due to a System of Stationary

Point Charges – Learning Objectives

1-2-1. Specific LearningObjectives:

1. Apply Coulomb's Law todetermine the electric fielddue to a stationary pointcharge.

2. Determine the net electricfield at a specified location inthe vicinity of a group ofstationary point charges;

3. Determine the net electricforce on a point charge at aspecified location in thevicinity of a group of pointcharges

4. Determine the electric force ona point charge in a region ofknown electric field strength


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1-2-2: Electric Fields due to a System of

Stationary Point Charges – Key Concepts

1-2-2. Key Concepts

(a) Descriptions of an Electric Field:

• An electric field exists at some

location in space if a test

charge placed at rest at thatlocation experiences an

electric force.

• The static electric field at any

specified location due to a

point charge must lie along theline connecting the charge to

the specified location


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1-2-2. Key Concepts

(a) The Electric Field (E) :

(i) The electric field due to a

charge q at a given location (P)

is derived from Coulomb's lawas the electric force (F) that

acts on a unit positive charge

q0 placed at P.

(ii) E points radially away from apositive charge; and

(iii) E points radially toward a

negative charge.


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1-2-2. Key Concepts

(b) The Electric Field (E) :

• The magnitude of the electric

field due to a point charge (q) at

a location from the charge isinversely proportional to the

square of the distance (r) from

the charge, and directly

proportional to the charge,

where

K = 9.0 x 109 N.m2/C2


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1-2-2. Key Concepts

(c) The Net Electric Field (E) :

• The net (or resultant) electric

field at a location due to a group

of electric charges in the vicinityis the vector sum of the electric

fields at that location due to the

individual charges present.

(d) The Electric Force ( F = qE) :

• The net (or resultant) electric field

existing at a location in space exerts

an electric force on any charge

placed at that location.

• The electric force exerted on a

positive charge (+q) points in the

same direction as the electric field;

• The electric force on a negative

charge (-q) points opposite to the

direction of the electric field at the

location.


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1-2-3: Visualizing Electric Fields (1)

1-2-3. Electric Fields

(a) Electric field patterns:

• The electric field in the region

surrounding a given point

(source) charge q can begraphically represented by the

field lines or lines of force.

• The electric field lines show the

directions of the force on a

( positive) test charge placed at a(field) point, a distance r from

the charge.


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(b) Electric field vector:

• The magnitude of the electric

field due to a charge q at point

P is given by:

• Point P is NOT a charge, but

merely a point in space, where

you test the field (with a test

+charge).

• The electric field points in the

direction of the force on a test

charge q0 placed at P .


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(c) Electric field lines:

• The electric field vector is

always tangent to the electric

field line at each (field) point.• The field lines are drawn from

positive charges and end on

negative charges

• For isolated (or excess) charges,

the field lines begin at infinityand end on a negative charge,

or begin from a positive charge

and end at infinity.


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(c) Electric field lines (contd.):

• No two field lines can intersect.

(Crossing lines indicate that the

electric field has two directionsat the point of intersection).

• The number of field lines drawn

from positive charges or ending

on negative charges is

proportional to the magnitudeof the charge.

• The number of field lines per unitarea through a surfaceperpendicular to the lines isproportional to the strength (ormagnitude) of the electric field in

that region.• A high field line density (where

field lines are close together)indicates a large electric field. Thefield lines are spaced far apart(low field line density) to indicate

a weak electric field.• Field lines are drawn

symmetrically for isolatedcharges


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(d) Motion of a Point Charge in an

Electric field:

• A point charge q in an electric

field E experiences an electricforce F,

• This force causes an acceleration

of the charged object of mass m:

• A positive charge is accelerated

in the same direction as the


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(d) Motion of a Point Charge in an

Electric field (contd.):

• electric field in that region. A

negatively-charged object will beaccelerated in the opposite

direction to the electric field.

• The equations of kinematics may

be applied to determine the

velocity and displacement of thecharge inside the electric field.


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1-2-4: Electrostatic Fields – Problem-solving Strategy

(1)

• Step 1: Apply Coulomb’s law to calculate themagnitude of each electric field (vector) strength at aspecified location due to each charge (as if it were theonly charge present);

• Step 2: Show the directions of the electric fields at thespecified observation point due to each charge present;the electric field at a point is in the same direction as thatof the force exerted on a positive test charge placed at

that point.• Step 3: Resolve each electric field vector into rectangular

x- and y-components.


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1-2-4: Electrostatic Fields – Problem-solving Strategy

(2)

• Step 4: By applying the Principle of Superposition offorces, find the resultant (net) field as the vector sum ofall the fields at the observation point; add similarcomponents to obtain the sum of the x-components and

the sum of the y-components of the resultant.

• Step 5: Using these x- and y-components of the resultantfield, sketch the resultant field vector. Apply

Pythagorean Theorem to find the magnitude of thisresultant vector and use the appropriate trigonometricratios to find the angle that defines the direction of theresultant electric field.


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1-2-5: Electric Fields due to a System of Stationary

Point Charges – Guided Problem-solving (1)

1-2 Electric Fields

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