AP Physics C
Electricity &
Magnetism
Review
Workbook
Name_____________________
, 1. Charge
a. Net – charge: excess electrons
b. Net + charge: excess “holes”
c. SI unit: coulomb (C)
d. Quantum of charge
i. the proton charge (e)
ii. the electron charge (-e)
−19
iii. 𝑒 = 1. 602 𝑥 10 𝐶
e. Conservation of Charge
i. The net charge in any process or reaction remains unchanged.
2. Coulomb’s Law
a. Calculates magnitude of force between charges
b. Force is repulsive if charges have the same sign.
c. Force is attractive if charges have opposite signs.
i. F = kq1q2/r2
1. F: force (N)
9 2 2
2. k: 9. 0 𝑥 10 𝑁𝑚 /𝐶
3. q1, q2: charges (C)
4. r: distance between charge centers (m)
−12 2 2
NOTE: 𝑘 = 1/4πϵ𝑜where ϵ𝑜 = 8. 85 𝑥 10 𝐶 /𝑁𝑚
d. Multiple Forces on a Charges
i. 𝐹𝑡𝑜𝑡𝑎𝑙 = Σ𝐹1
A. As shown above, two particles, each of charge +Q,
are fixed at opposite corners of a square that lies in
the plane of the page. A positive test charge +q is
placed at a third corner. What is the direction of the
force on the test charge due to the two other
charges?
Explain your reasoning
B. If F is the magnitude of the force on the test
charge due to only one of the other charges, what is
the magnitude of the net force acting on the test
charge due to both of these charges?
Show your work
C. Suppose that an electron (charge ‑e) could orbit a
proton (charge +e) in a circular orbit of constant
radius R. Assuming that the proton is stationary and
only electrostatic forces act on the particles, write an
equation that represents the kinetic energy of the
two‑particle system.
Show your work
D. Two small spheres have equal charges q and are
separated by a distance d. The force exerted on each
sphere by the other has magnitude F. If the charge
, on each sphere is doubled and d is halved, the force
on each sphere has magnitude
Show your work
3. Electric Field
a. Exists in space due to the presence of charge.
b. Predicts what will happen to a charged particle put in that location in space.
c. Points in the direction that a positive test charge would be forced.
i. Field is directed outward from the positive charges creating it.
ii. Field is directed inward toward the negative charge creating it.
d. The magnitude of field at point in space near one spherically symmetric charge:
2
i. 𝐸 = 𝑘𝑞/𝑟 (magnitude calculation)
1. E: field (N/C)
9 2 2
2. k: 9. 0 𝑥 10 𝑁𝑚 /𝐶
3. q: charge (C)
4. r: distance between center of charge and point in space (m)
ii. The equation above works only for spherically symmetric charge distributions.
NOTE:Positive charges experience a force in the same direction as the electric field is pointing. Negative
charges experience a force in the opposite direction as the electric field.
E. Two initially uncharged conductors, 1 and 2, are
mounted on insulating stands and are in contact, as
shown above. A negatively charged rod is brought
near but does not touch them. With the rod held in
place, conductor 2 is moved to the right by pushing
its stand, so that the conductors are separated. What
if any, is the charge distribution on each sphere?
Explain your reasoning
F. Two metal spheres that are initially uncharged are
mounted on insulating stands, as shown above. A
negatively charged rubber rod is brought close to,
but does not make contact with, sphere X. Sphere Y
is then brought close to X on the side opposite to the
rubber rod. Y is allowed to touch X and then is
removed some distance away. The rubber rod is then
moved far away from X and Y. What are the final
charges on the spheres?
Explain your reasoning
G. From the electric field vector at a point, one can
determine which of the following?
I. The direction of the electrostatic force on a test
charge of known sign at that point
Electricity &
Magnetism
Review
Workbook
Name_____________________
, 1. Charge
a. Net – charge: excess electrons
b. Net + charge: excess “holes”
c. SI unit: coulomb (C)
d. Quantum of charge
i. the proton charge (e)
ii. the electron charge (-e)
−19
iii. 𝑒 = 1. 602 𝑥 10 𝐶
e. Conservation of Charge
i. The net charge in any process or reaction remains unchanged.
2. Coulomb’s Law
a. Calculates magnitude of force between charges
b. Force is repulsive if charges have the same sign.
c. Force is attractive if charges have opposite signs.
i. F = kq1q2/r2
1. F: force (N)
9 2 2
2. k: 9. 0 𝑥 10 𝑁𝑚 /𝐶
3. q1, q2: charges (C)
4. r: distance between charge centers (m)
−12 2 2
NOTE: 𝑘 = 1/4πϵ𝑜where ϵ𝑜 = 8. 85 𝑥 10 𝐶 /𝑁𝑚
d. Multiple Forces on a Charges
i. 𝐹𝑡𝑜𝑡𝑎𝑙 = Σ𝐹1
A. As shown above, two particles, each of charge +Q,
are fixed at opposite corners of a square that lies in
the plane of the page. A positive test charge +q is
placed at a third corner. What is the direction of the
force on the test charge due to the two other
charges?
Explain your reasoning
B. If F is the magnitude of the force on the test
charge due to only one of the other charges, what is
the magnitude of the net force acting on the test
charge due to both of these charges?
Show your work
C. Suppose that an electron (charge ‑e) could orbit a
proton (charge +e) in a circular orbit of constant
radius R. Assuming that the proton is stationary and
only electrostatic forces act on the particles, write an
equation that represents the kinetic energy of the
two‑particle system.
Show your work
D. Two small spheres have equal charges q and are
separated by a distance d. The force exerted on each
sphere by the other has magnitude F. If the charge
, on each sphere is doubled and d is halved, the force
on each sphere has magnitude
Show your work
3. Electric Field
a. Exists in space due to the presence of charge.
b. Predicts what will happen to a charged particle put in that location in space.
c. Points in the direction that a positive test charge would be forced.
i. Field is directed outward from the positive charges creating it.
ii. Field is directed inward toward the negative charge creating it.
d. The magnitude of field at point in space near one spherically symmetric charge:
2
i. 𝐸 = 𝑘𝑞/𝑟 (magnitude calculation)
1. E: field (N/C)
9 2 2
2. k: 9. 0 𝑥 10 𝑁𝑚 /𝐶
3. q: charge (C)
4. r: distance between center of charge and point in space (m)
ii. The equation above works only for spherically symmetric charge distributions.
NOTE:Positive charges experience a force in the same direction as the electric field is pointing. Negative
charges experience a force in the opposite direction as the electric field.
E. Two initially uncharged conductors, 1 and 2, are
mounted on insulating stands and are in contact, as
shown above. A negatively charged rod is brought
near but does not touch them. With the rod held in
place, conductor 2 is moved to the right by pushing
its stand, so that the conductors are separated. What
if any, is the charge distribution on each sphere?
Explain your reasoning
F. Two metal spheres that are initially uncharged are
mounted on insulating stands, as shown above. A
negatively charged rubber rod is brought close to,
but does not make contact with, sphere X. Sphere Y
is then brought close to X on the side opposite to the
rubber rod. Y is allowed to touch X and then is
removed some distance away. The rubber rod is then
moved far away from X and Y. What are the final
charges on the spheres?
Explain your reasoning
G. From the electric field vector at a point, one can
determine which of the following?
I. The direction of the electrostatic force on a test
charge of known sign at that point
