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WorksheetsAP Physics C - Electrostatics
Total questions: 20
Worksheet time: 2hrs 40mins
A metal sphere with radius r1 has a total electric charge of magnitude q. An uncharged metal sphere with radius r2 (with r1 > r2) is then connected by a wire to the first sphere, as illustrated above. The separation of the spheres is much greater than the radius of either sphere. When equilibrium is reached, the spheres will have
charges on their surfaces of equal magnitude and the same sign
charges on their surfaces of equal magnitude and opposite sign
equal electric fields at their surfaces
equal capacitances
equal electric potentials
A positive electric charge is moved at a constant speed between two locations in an electric field, with no work done by or against the field at any time during the motion. This situation can occur only if the
charge is moved in the direction of the field
charge is moved opposite to the direction of the field
charge is moved perpendicular to an equipotential line
charge is moved along an equipotential line
electric field is uniform
A proton moving along the positive x-axis enters an electric field that is directed along the positive y-axis. What is the direction of the electric force acting on the proton after it enters the electric field?
along the negative z-axis
along the positive z-axis
along the negative y-axis
along the positive y-axis
The direction cannot be determined since the magnitude of the electric field is not known
A capacitor is constructed of two identical conducting plates parallel to each other and separated by a distance d. The capacitor is charged to a potential difference of V0 by a battery, which is then disconnected.
A sheet of insulating plastic material is inserted between the plates without otherwise disturbing the system. What effect does this have on the capacitance?
It causes the capacitance to increase
It causes the capacitance to decrease
None; the capacitance does not change
Nothing can be said about the effect without knowing the dielectric constant of the plastic
Nothing can be said about the effect without knowing the thickness of the sheet.
Two small spheres are arranged along a line and carry charges of +4Q and –3Q, as shown in the figure above. The vertical lines are equally spaced.
At which of the labeled points does the electric field point toward the right with the smallest magnitude?
A
B
C
D
E
A charge +𝑄 is inside a hollow region in an electrically neutral piece of solid metal, as shown above. The dashed line represents a Gaussian surface within the metal that completely encloses the hollow region.
At which of the three labeled points is the electric field equal to zero?
X only
Y only
X and Z only
Y and Z only
X, Y, and Z
The conducting sphere in Figure 1 has a charge of −Q
and is electrically isolated so that there is no conducting path to or from the conducting object shown in Figure 2. The charges on the sphere are in equilibrium. The same charge −Q
is on the isolated conducting object. Which of the following correctly describes a change between the sphere in Figure 1 and the object in Figure 2?
The charge is no longer located entirely on the surface of the object.
The electric field inside the object is no longer zero everywhere
The electric potential is no longer the same at all points inside the object.
The electric field is no longer directed perpendicular to the surface at all points on the object
The magnitude of the electric field is no longer the same at all points on the surface
If the only force acting on an electron is due to a uniform electric field, the electron moves with constant
acceleration in a direction opposite to that of the field
acceleration in the direction of the field
acceleration in a direction perpendicular to that of the field
speed in a direction opposite to that of the field
speed in the direction of the field
A battery or batteries connected to two parallel plates produce the equipotential lines between the plates shown above.
The force on an electron located on the 0-volt potential line is
0 N
1 N, directed to the right
1 N, directed to the left
directed to the right, but its magnitude cannot be determined without knowing the the distance between the lines
directed to the left, but its magnitude cannot be determined without knowing the distance between the lines
A battery or batteries connected to two parallel plates produce the equipotential lines between the plates shown above.
The force on an electron located on the 0-volt potential line is
Q2 = 16Q1
Q2 = 4Q1
Q2 = Q1
Q2 = 0.25Q1
The above circuit is designed with an ideal battery and a capacitor. When the capacitor is fully charged, the charge on the capacitor plates has a magnitude Q. Which of the following is a correct hypothesis for what will happen to the capacitor when a material of dielectric constant κ is inserted between the capacitor plates?
The charge stored on the capacitor will increase
The charge stored on the capacitor will decrease
The potential difference across the plates of the capacitor will increase
The potential difference across the plate of the capacitor will decrease
The energy stored on the capacitor will remain the same
A capacitor with unknown capacitance is used for an experiment. Students connect the capacitor to a battery, allow the capacitor to become fully charged, and then isolate the capacitor. The students then insert dielectrics with different dielectric constants κ, one at a time, between the plates of the capacitor and measure the potential difference V across the capacitor. Which of the following hypotheses can be tested with this data?
For a given the potential difference V, the charge stored in a capacitor will increase as the dielectric constant of the material between the plates increases.
For a given the potential difference V, the energy stored in a capacitor will increase as the dielectric constant of the material between the plates increases.
For a given the potential difference V, the charge stored in a capacitor will increase as the capacitance of the capacitor increases.
For a given stored charge, the breakdown voltage of a capacitor will decrease as the dielectric constant of the material between the plates increases.
For a given stored charge, the potential difference across the plates of a capacitor will increase as the dielectric constant of the material between the plates increases.
If a dielectric is inserted between the plates of a capacitor while the capacitor maintains its connection to a constant voltage source, which of the following is true?
The capacitance of the capacitor is unchanged
The charge on the capacitor plates increases
The potential difference across the capacitor increases
The electric field between the capacitor plates increases
The electric field between the capacitor plates decreases
A hollow conducting sphere is surrounded by a larger concentric spherical conducting shell, as shown above. The inner sphere has a net charge of –Q, and the outer sphere has a net charge of +3Q.
What is the net charge on the outer surface of the spherical shell?
0
+Q
+2Q
+3Q
+4Q
A solid, conducting sphere with zero net charge is placed into a uniform electric field. Which of the following happens immediately after the sphere is placed in the field?
An electric field is momentarily set up on the conducting sphere, redistributing the charges until the surface again becomes equipotential.
A nonuniform electric field is permanently set up inside the conducting sphere, pushing charges to the surface of the sphere.
The external electric field redistributes the charges evenly inside the sphere, resulting in the electric field becoming zero inside the sphere.
The electric field aligns the charges inside the sphere in such a way that they create a uniform electric field inside the sphere that is equivalent to the external electric field.
The electric field does not interact with the sphere since it has zero net charge.
When two metal objects, X and Y, are connected to each other by a conducting wire, object X gains electrons. From this information, it can be inferred that before the connection was made, object X, compared with object Y, must have had
less capacitance
more electrical potential energy
a smaller dielectric constant
a greater electric charge
a greater electric potential
A uniform electric field exists in which of the following regions?
I. Around an infinite line of uniform linear charge density
II. On either side of an infinite thin sheet of uniform charge density
III. Between the spherical shells of a charged spherical capacitor
I only
II only
III only
II and III only
I, II, and III
The figure above shows an object in the shape of an arc. The object has a uniform charge distribution. The three labeled vectors show possible directions of the electric field at point P
at the center of the arc. Which of the following options indicates the vector that shows the correct direction of the electric field and provides a correct physical explanation for this direction?
Vector A: the charge distribution is positive, and there are more charges to the left of point P
.
Vector A: the charge distribution is negative, and there are more charges to the left of point P
.
Vector B: the charge distribution is positive, and there are more charges above point P
.
Vector B: the charge distribution is negative, and there are more charges above point P
.
Vector C: the charge distribution is positive, and there are no charges below and to the left of point P
to cancel the field from charges above and to the right of point P
.
Which of the following must be true for a Gaussian surface through which the net flux is zero?
I. There are no charges inside the surface.
II. The net charge enclosed by the surface is zero.
III. The electric field is zero everywhere on the surface.
I only
II only
III only
I and II only
I, II, and III
The graph above shows the electric field E as a function of x, where x is the distance from a given charge arrangement in an xyz-coordinate system. Which of the following could be the arrangement?
A positive point charge at x = 0
Positive charges uniformly distributed inside a sphere with x = 0 on the sphere’s surface
Positive charges uniformly distributed on the surface of a sphere with x = 0 on the sphere’s surface
Positive charges uniformly distributed along the y-axis
Positive charges uniformly distributed over the yz-plane
