Name: _______________________________
Electric Fields and Dipoles – Practice
1. The electric field lines on the left have twice the
separation of those on the right.
A. If the magnitude of the field at A is 40 N/C, what
is the magnitude of the force on a proton at A?
B. What is the magnitude of the field at B?
2. The nucleus of a plutonium-239 atom contains 94 protons. Assume that the nucleus is a
sphere with radius 6.64 fm and with the charge of the protons uniformly spread through
the sphere. At the nucleus surface, what are the magnitude and direction (radially inward
or outward) of the electric field produced by the protons?
3. Two particles are attached to an x axis: particle 1 of charge -2.00 × 10-7 C at x = 6.00 cm,
particle 2 of charge +2.00 × 10-7 C at x = 21.0 cm. Midway between the particles, what is
their net electric field in unit-vector notation?
4. Two charged particles are on the x axis: -q = -3.20 × 10-19 C at x =
-3.00 m and q = 3.20 × 10-19 C at x = +3.00 m. What are the
magnitude and direction (relative to the positive direction of the
x axis) of the net electric field produced at point P at y = 4.00 m?
5. An uneven arrangement of electrons (e) and protons (p)
exists on a circular arc of radius r = 2.00 cm, with angles
θ1 = 30.0°, θ2 = 50.0°, θ3 = 30.0°, and θ4 = 20.0°. What
are the magnitude and direction (relative to the positive
direction of the x axis) of the net electric field produced
at the center of the arc?
Solutions:

1. A. 6.4 x 10-18 N to left
3. E   6.39 x 105
N
î
C
B. 20 N/C
2. 3.07 x 1021 N/C radially outward
4. 1.38 x 10-10 N/C to left
5. 3.93 x 10-6 N/C @ -76.4o
Examples Of Finding Electric Fields With Integration
I. Key Equation:
E =

dE 

k dq
r2
II. Problems
-Q
dx
A. Uniformly Charged Rod
1. Linear charge density:  =
L
Q
[
L
]
2. dq = _________ [ C ]
3. Suggest a material that this rod could be made from: _____________
4. Find the electric field at point P.
dx
P
L
L
-Q
B. Uniformly Charged Circular Arc
1. Linear charge density:  = _________ [
]
r
2. dq = ____________ = ____________ [
3. E =

dEx 

dE cos

4. E =



dE cos
=


k dq
r2
and

cos =
]
d
P

ds = r d

dEy  0 . Why?
-Q
C. Uniformly Charged Disk
1. Surface charge density:  = ________ [
]
R
r
2. dA = _________
3. Find the area of the circle using A =
Q


dA
dA
dr
4. dq = _________ [ C ]
5. What is the direction of the electric field very near the surface of the disk? (The
disk is seen edge on it the figure below.)
6. What is the direction of the electric field very far from the disk (i.e outside of the
dotted lines)?
D. Uniformly Charged Sphere
A nonconducting sphere of radius R contains a total charge of
Q distributed uniformly throughout its volume (e.g. its volume
1. Volume charge density:  = ________ [
2. dV = _________
3. Find the volume of the sphere using V =

R
r
]
dV
Q

dV
dr
4. dq = _________ [ C ]
5. What is the enclosed charge Qenclosed (i.e. the charge inside the radius r) in terms of
the total charge Q.
6. What is the magnitude of the electric field at a radius r when r <=R in terms of the
total charge Q?
7. What is the magnitude of the electric field at a radius r when r <=R in terms of the
charge density  ?
8. What is the magnitude of the electric field at a radius r when r > R?
9. Draw the graph of E versus r that includes the field both the inside and outside.