Conductors, Capacitors, Dielectrics Free Response Practice Questions | AP Physics C Electricity and Magnetism - Grade 9 PDF Download

 Page 1


Section II: Free Response
1. In the figure shown, all four charges are situated at the corners of a square with sides s.
(a) What is the total electrical potential energy of this array of fixed charges?
(b) What is the electric field at the center of the square?
(c) What is the electric potential at the center of the square?
(d) Sketch (on the diagram) the portion of the equipotential surface that lies in the plane of the
figure and passes through the center of the square.
(e) How much work would the electric field perform on a charge q as it moved from the
midpoint of the right side of the square to the midpoint of the top of the square?
2. The figure below shows a parallel-plate capacitor. Each rectangular plate has length L and
width w, and the plates are separated by a distance d.
(a) Determine the capacitance.
An electron (mass m, charge -e) is shot horizontally into the empty space between the plates,
midway between them, with an initial velocity of magnitude v
0
. The electron just barely misses
hitting the end of the top plate as it exits. (Ignore gravity.)
Page 2


Section II: Free Response
1. In the figure shown, all four charges are situated at the corners of a square with sides s.
(a) What is the total electrical potential energy of this array of fixed charges?
(b) What is the electric field at the center of the square?
(c) What is the electric potential at the center of the square?
(d) Sketch (on the diagram) the portion of the equipotential surface that lies in the plane of the
figure and passes through the center of the square.
(e) How much work would the electric field perform on a charge q as it moved from the
midpoint of the right side of the square to the midpoint of the top of the square?
2. The figure below shows a parallel-plate capacitor. Each rectangular plate has length L and
width w, and the plates are separated by a distance d.
(a) Determine the capacitance.
An electron (mass m, charge -e) is shot horizontally into the empty space between the plates,
midway between them, with an initial velocity of magnitude v
0
. The electron just barely misses
hitting the end of the top plate as it exits. (Ignore gravity.)
(b) In the diagram, sketch the electric field vector at the position of the electron when it has
traveled a horizontal distance of L/2.
(c) In the diagram, sketch the electric force vector on the electron at the same position as in
part (b).
(d) Determine the strength of the electric field between the plates. Write your answer in terms
of L, d, m, e, and v
0
.
(e) Determine the charge on the top plate.
(f) How much potential energy is stored in the capacitor?
3. A solid conducting sphere of radius a carries an excess charge of Q.
(a) Determine the electric field magnitude, E(r), as a function of r, the distance from the
sphere’s center.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). (Cover at least the range 0 < r < 2a.)
4. A solid, nonconducting sphere of radius a has a volume charge density given by the
equation ?(r) = ?
0
(r/a)
3
, where r is the distance from the sphere’s center.
(a) Determine the electric field magnitude, E(r), as a function of r.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). Be sure to indicate on the vertical axis in each
plot the value at r = a.
Page 3


Section II: Free Response
1. In the figure shown, all four charges are situated at the corners of a square with sides s.
(a) What is the total electrical potential energy of this array of fixed charges?
(b) What is the electric field at the center of the square?
(c) What is the electric potential at the center of the square?
(d) Sketch (on the diagram) the portion of the equipotential surface that lies in the plane of the
figure and passes through the center of the square.
(e) How much work would the electric field perform on a charge q as it moved from the
midpoint of the right side of the square to the midpoint of the top of the square?
2. The figure below shows a parallel-plate capacitor. Each rectangular plate has length L and
width w, and the plates are separated by a distance d.
(a) Determine the capacitance.
An electron (mass m, charge -e) is shot horizontally into the empty space between the plates,
midway between them, with an initial velocity of magnitude v
0
. The electron just barely misses
hitting the end of the top plate as it exits. (Ignore gravity.)
(b) In the diagram, sketch the electric field vector at the position of the electron when it has
traveled a horizontal distance of L/2.
(c) In the diagram, sketch the electric force vector on the electron at the same position as in
part (b).
(d) Determine the strength of the electric field between the plates. Write your answer in terms
of L, d, m, e, and v
0
.
(e) Determine the charge on the top plate.
(f) How much potential energy is stored in the capacitor?
3. A solid conducting sphere of radius a carries an excess charge of Q.
(a) Determine the electric field magnitude, E(r), as a function of r, the distance from the
sphere’s center.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). (Cover at least the range 0 < r < 2a.)
4. A solid, nonconducting sphere of radius a has a volume charge density given by the
equation ?(r) = ?
0
(r/a)
3
, where r is the distance from the sphere’s center.
(a) Determine the electric field magnitude, E(r), as a function of r.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). Be sure to indicate on the vertical axis in each
plot the value at r = a.
Page 4


Section II: Free Response
1. In the figure shown, all four charges are situated at the corners of a square with sides s.
(a) What is the total electrical potential energy of this array of fixed charges?
(b) What is the electric field at the center of the square?
(c) What is the electric potential at the center of the square?
(d) Sketch (on the diagram) the portion of the equipotential surface that lies in the plane of the
figure and passes through the center of the square.
(e) How much work would the electric field perform on a charge q as it moved from the
midpoint of the right side of the square to the midpoint of the top of the square?
2. The figure below shows a parallel-plate capacitor. Each rectangular plate has length L and
width w, and the plates are separated by a distance d.
(a) Determine the capacitance.
An electron (mass m, charge -e) is shot horizontally into the empty space between the plates,
midway between them, with an initial velocity of magnitude v
0
. The electron just barely misses
hitting the end of the top plate as it exits. (Ignore gravity.)
(b) In the diagram, sketch the electric field vector at the position of the electron when it has
traveled a horizontal distance of L/2.
(c) In the diagram, sketch the electric force vector on the electron at the same position as in
part (b).
(d) Determine the strength of the electric field between the plates. Write your answer in terms
of L, d, m, e, and v
0
.
(e) Determine the charge on the top plate.
(f) How much potential energy is stored in the capacitor?
3. A solid conducting sphere of radius a carries an excess charge of Q.
(a) Determine the electric field magnitude, E(r), as a function of r, the distance from the
sphere’s center.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). (Cover at least the range 0 < r < 2a.)
4. A solid, nonconducting sphere of radius a has a volume charge density given by the
equation ?(r) = ?
0
(r/a)
3
, where r is the distance from the sphere’s center.
(a) Determine the electric field magnitude, E(r), as a function of r.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). Be sure to indicate on the vertical axis in each
plot the value at r = a.
Section II: Free Response
1. (a) Labeling the four charges as given in the diagram, we get
(b) Let E
i
 denote the electric field at the center of the square due to charge i. Then by
symmetry, E
1
 = E
3
, E
2
 = E
4
, and E
1
 = E
2
 = E
3
 = E
4
. The horizontal components of the
four individual field vectors cancel, leaving only a downward-pointing electric field of
magnitude E
total
 = 4E
1
 cos 45°:
Page 5


Section II: Free Response
1. In the figure shown, all four charges are situated at the corners of a square with sides s.
(a) What is the total electrical potential energy of this array of fixed charges?
(b) What is the electric field at the center of the square?
(c) What is the electric potential at the center of the square?
(d) Sketch (on the diagram) the portion of the equipotential surface that lies in the plane of the
figure and passes through the center of the square.
(e) How much work would the electric field perform on a charge q as it moved from the
midpoint of the right side of the square to the midpoint of the top of the square?
2. The figure below shows a parallel-plate capacitor. Each rectangular plate has length L and
width w, and the plates are separated by a distance d.
(a) Determine the capacitance.
An electron (mass m, charge -e) is shot horizontally into the empty space between the plates,
midway between them, with an initial velocity of magnitude v
0
. The electron just barely misses
hitting the end of the top plate as it exits. (Ignore gravity.)
(b) In the diagram, sketch the electric field vector at the position of the electron when it has
traveled a horizontal distance of L/2.
(c) In the diagram, sketch the electric force vector on the electron at the same position as in
part (b).
(d) Determine the strength of the electric field between the plates. Write your answer in terms
of L, d, m, e, and v
0
.
(e) Determine the charge on the top plate.
(f) How much potential energy is stored in the capacitor?
3. A solid conducting sphere of radius a carries an excess charge of Q.
(a) Determine the electric field magnitude, E(r), as a function of r, the distance from the
sphere’s center.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). (Cover at least the range 0 < r < 2a.)
4. A solid, nonconducting sphere of radius a has a volume charge density given by the
equation ?(r) = ?
0
(r/a)
3
, where r is the distance from the sphere’s center.
(a) Determine the electric field magnitude, E(r), as a function of r.
(b) Determine the potential, V(r), as a function of r. Take the zero of potential at r = 8.
(c) On the diagrams below, sketch E(r) and V(r). Be sure to indicate on the vertical axis in each
plot the value at r = a.
Section II: Free Response
1. (a) Labeling the four charges as given in the diagram, we get
(b) Let E
i
 denote the electric field at the center of the square due to charge i. Then by
symmetry, E
1
 = E
3
, E
2
 = E
4
, and E
1
 = E
2
 = E
3
 = E
4
. The horizontal components of the
four individual field vectors cancel, leaving only a downward-pointing electric field of
magnitude E
total
 = 4E
1
 cos 45°:
(c) The potential at the center of the square is zero:
(d) At every point on the center horizontal line shown, r
1
 = r
4
 and r
2
 = r
3
, so V will equal zero
(just as it does at the center of the square):