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WorksheetsAP Physics C E&M
Total questions: 82
Worksheet time: 47mins
A current carrying loop of wire lies flat on a table top. When viewed from above, the current moves around the loop in a counterclockwise sense.
For points OUTSIDE the loop, the magnetic field caused by this current
circles the loop in a clockwise direction.
circles the loop in a counterclockwise direction.
points straight up.
points straight down.
is zero.
A current carrying loop of wire lies flat on a table top. When viewed from above, the current moves around the loop in a counterclockwise sense.
For points INSIDE the loop, the magnetic field caused by this current
circles the loop in a clockwise direction.
circles the loop in a counterclockwise direction.
points straight up.
points straight down.
is zero.
A horizontal wire carries a current straight toward you. From your point of view, the magnetic field at a point directly below the wire points
vertically upward.
directly toward you.
to the right.
to the left.
directly away from you.
An electron moving in the direction of the +x-axis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, the direction of the magnetic field in this region points in the direction of the
+z-axis.
-z-axis.
-x-axis.
+y-axis.
-y-axis.
Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively,
1 is neutral, 2 is negative, and 3 is positive.
1 is neutral, 2 is positive, and 3 is negative.
1 is positive, 2 is neutral, and 3 is negative.
1 is positive, 2 is negative, and 3 is neutral.
1 is negative, 2 is neutral, and 3 is positive.
A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc?
9R
3R
√3 R
R / √3
R / 9
Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?
4R
3R
√2 R
R / √2
R / 2
A charged particle is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. If the frequency of revolution of the first particle is f, the frequency of revolution of the second particle is
f
2f
4f
f / 2
f / 4
Two long parallel wires placed side-by-side on a horizontal table carry identical size currents in opposite directions. The wire on your right carries current toward you, and the wire on your left carries current away from you. From your point of view, the magnetic field at the point exactly midway between the two wires
points upward.
points downward.
points toward you.
points away from you
is zero.
The figure shows two long wires carrying equal currents I1 and I2 flowing in opposite directions. Which of the arrows labeled A through D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire?
A
B
C
D
E
A negatively charged particle is moving to the right, directly above a wire having a current flowing to the right, as shown in the figure. In which direction is the magnetic force exerted on the particle?
into the page
out of the page
downward
upward
The magnetic force is zero since the velocity is parallel to the current.
Two very long parallel wires are a distance d apart and carry equal currents in opposite directions. The locations where the net magnetic field due to these currents is equal to zero are
midway between the wires.
a distance d/2 to the left of the left wire and also a distance d/2 to the right of the right wire.
a distance d/√2 to the left of the left wire and also a distance d/√2 to the right of the right wire.
a distance d to the left of the left wire and also a distance d to the right of the right wire.
The net field is not zero anywhere.
The figure shows three long, parallel current-carrying wires. The magnitudes of the currents are equal and their directions are indicated in the figure. Which of the arrows drawn near the wire carrying current 1 correctly indicates the direction of the magnetic force acting on that wire?
A
B
C
D
A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure). Which of the following statements is true?
The net magnetic force on the wire rectangle is upward, and there is also a net torque on the it.
The net magnetic force on the wire rectangle is zero, and the net torque on it is zero.
The net magnetic force on the wire rectangle is downward, and there is also a net torque on the it.
The net magnetic force on the wire rectangle is zero, but there is a net torque on it.
The net magnetic force on the wire rectangle is downward, and the net torque on it is zero.
A very long, hollow, thin-walled conducting cylindrical shell (like a pipe) of radius R carries a current along its length uniformly distributed throughout the thin shell. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?
A very long, solid, conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?
Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the radius of the solenoid were doubled (becoming 2b), and all other quantities remained the same, the magnetic field inside the solenoid would A) B) C)
remain the same.
become twice as strong.
become one half as strong.
Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the length of the solenoid became twice as long (2L), and all other quantities remained the same, the magnetic field inside the solenoid would
remain the same.
become twice as strong.
become one half as strong.
As more resistors are added in parallel across a constant voltage source, the power supplied by the source
increases.
decreases.
does not change.
The figure shows three identical lightbulbs connected to a battery having a constant voltage across its terminals. What happens to the brightness of lightbulb 1 when the switch S is closed?
The brightness will increase momentarily then return to its previous level.
The brightness increases permanently.
The brightness will decrease momentarily then return to its previous level.
The brightness remains the same as before the switch is closed.
The brightness decreases permanently.
In the circuit shown in the figure, all the lightbulbs are identical. Which of the following is the correct ranking of the brightness of the bulbs?
B and C have equal brightness, and A is the dimmest.
A is brightest, C is dimmest, and B is in between.
A and B have equal brightness, and C is the dimmest.
A is the brightest, and B and C have equal brightness but less than A.
All three bulbs have the same brightness.
A light bulb is connected in the circuit shown in the figure with the switch S open. All the connecting leads have no appreciable resistance and the battery has no internal resistance. When we close the switch, which statements below accurately describe the behavior of the circuit? (There may be more than one correct choice.)
The brightness of the bulb will increase.
The brightness of the bulb will decrease.
The brightness of the bulb will not change.
The potential drop across R2 will decrease.
The potential drop across R2 will not change.
A resistor and a capacitor are connected in series across an ideal battery having a constant voltage across its terminals. At the moment contact is made with the battery, the voltage across the capacitor is
equal to the battery's terminal voltage.
less than the battery's terminal voltage, but greater than zero.
equal to the battery's terminal voltage.
zero.
A resistor and a capacitor are connected in series across an ideal battery having a constant voltage across its terminals. At the moment contact is made with the battery the voltage across the resistor is
equal to the battery's terminal voltage.
less than the battery's terminal voltage, but greater than zero.
equal to the battery's terminal voltage.
zero.
An RC circuit is connected across an ideal DC voltage source through an open switch. The switch is closed at time t = 0 s. Which of the following statements regarding the circuit are correct? (There may be more than one correct choice.)
The capacitor charges to its maximum value in one time constant and the current is zero at that time.
The potential difference across the resistor and the potential difference across the capacitor are always equal.
The potential difference across the resistor is always greater than the potential difference across the capacitor.
The potential difference across the capacitor is always greater than the potential difference across the resistor
Once the capacitor is essentially fully charged, there is no appreciable current in the circuit.
A light bulb is connected in the circuit shown in the figure with the switch S open and the capacitor uncharged. The battery has no appreciable internal resistance. Which one of the following graphs best describes the brightness B of the bulb as a function of time t after closing the switch?
A wire of resistivity ρ must be replaced in a circuit by a wire of the same material but 4 times as long. If, however, the resistance of the new wire is to be the same as the resistance of the original wire, the diameter of the new wire must be
2 times the diameter of the original wire.
4 times the diameter of the original wire.
the same as the diameter of the original wire.
1/2 the diameter of the original wire.
1/4 the diameter of the original wire.
A metallic sphere of radius 5 cm is charged such that the potential of its surface is 100 V (relative to infinity). Which of the following plots correctly shows the potential as a function of distance from the center of the sphere? (Ignore the W, X, Y, and Z on the plots.)
A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere?
A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)
The potential is highest at the center of the sphere.
The potential at the center of the sphere is zero.
The potential at the center of the sphere is the same as the potential at the surface.
The potential at the surface is higher than the potential at the center.
The potential at the center is the same as the potential at infinity.
A conducting sphere contains positive charge distributed uniformly over its surface. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)
The potential is lowest, but not zero, at the center of the sphere.
The potential at the center of the sphere is zero.
The potential at the center of the sphere is the same as the potential at the surface.
The potential at the surface is higher than the potential at the center.
The potential at the center is the same as the potential at infinity.
The graph in the figure shows the variation of the electric potential V(x) (in arbitrary units) as a function of the position x (also in arbitrary units). Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis?
Ex is positive from x = -2 to x = 2.
Ex is positive from x = -2 to x = 0, and negative from x = 0 to x = 2.
Ex is negative from x = -2 to x = 0, and positive from x = 0 to x = 2.
Ex is negative from x = -2 to x = 2
The potential as a function of position x is shown in the graph in the figure. Which statement about the electric field is true?
The electric field is zero at x = 0, its magnitude is at a maximum at x = 5 cm, and the field is directed to the right there. B) C) D)
The electric field is zero at x = 5 cm, its magnitude is at a maximum at x = 0, and the field is directed to the right there.
The electric field is zero at x = 0, its magnitude is at a maximum at x = 15 cm, and the field is directed to the left there.
The electric field is zero at x = 10 cm, its magnitude is at a maximum at x = 5 cm, and the field is directed to the left there.
The charge on the square plates of a parallel-plate capacitor is Q. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The amount of charge on the plates is now equal to
4Q.
2Q.
Q.
Q/2.
Q/4.
The electric field between square the plates of a parallel-plate capacitor has magnitude E. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The magnitude of the electric field between the plates is now equal to
4E.
2E.
E.
E/2.
E/4
Equal but opposite charges Q are placed on the square plates of an air-filled parallel-plate capacitor. The plates are then pulled apart to twice their original separation, which is small compared to the dimensions of the plates. Which of the following statements about this capacitor are true? (There may be more than one correct choice.)
The energy stored in the capacitor has doubled.
The energy density in the capacitor has increased.
The electric field between the plates has increased.
The potential difference across the plates has doubled.
The capacitance has doubled.
When two or more capacitors are connected in series across a potential difference,
the potential difference across the combination is the algebraic sum of the potential differences across the individual capacitors.
each capacitor carries the same amount of charge.
the equivalent capacitance of the combination is less than the capacitance of any of the capacitors.
All of the choices are correct.
None of the above choices are correct.
An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d. When this capacitor is connected to a battery that maintains a constant potential difference between the plates, the energy stored in the capacitor is U0. If the separation between the plates is doubled, how much energy is stored in the capacitor?
4U0
2U0
U0
U0/2
U0/4
An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d. When the capacitor plates carry charges +Q and -Q, the capacitor stores energy U0. If the separation between the plates is doubled, how much electrical energy is stored in the capacitor?
4U0
2U0
U0
U0/2
U0/4
If the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.
True
False
When the electric field is zero at a point, the potential must also be zero there.
True
False
If the electrical potential in a region is constant, the electric field must be zero everywhere in that region.
True
False
If the electric potential at a point in space is zero, then the electric field at that point must also be zero.
True
False
A negative charge, if free, will tend to move
from high potential to low potential.
from low potential to high potential.
toward infinity.
away from infinity.
in the direction of the electric field.
Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure. Which statement about the electric potential is true?
The potential at all three locations (A, B, C) is the same because the field is uniform.
The potential at points A and B are equal, and the potential at point C is higher than the potential at point A.
The potential at points A and B are equal, and the potential at point C is lower than the potential at point A.
The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest.
Which statements are true for an electron moving in the direction of an electric field? (There may be more than one correct choice.)
Its electric potential energy increases as it goes from high to low potential.
Its electric potential energy decreases as it goes from high to low potential.
Its potential energy increases as its kinetic energy decreases.
Its kinetic energy decreases as it moves in the direction of the electric field.
Its kinetic energy increases as it moves in the direction of the electric field.
Suppose you have two point charges of opposite sign. As you move them farther and farther apart, the potential energy of this system relative to infinity
increases.
decreases.
stays the same.
Suppose you have two negative point charges. As you move them farther and farther apart, the potential energy of this system relative to infinity
increases.
decreases.
stays the same.
Two equal positive charges are held in place at a fixed distance. If you put a third positive charge midway between these two charges, its electrical potential energy of the system (relative to infinity) is zero because the electrical forces on the third charge due to the two fixed charges just balance each other.
True
False
A negative charge is moved from point A to point B along an equipotential surface. Which of the following statements must be true for this case?
The negative charge performs work in moving from point A to point B.
Work is required to move the negative charge from point A to point B.
No work is required to move the negative charge from point A to point B.
The work done on the charge depends on the distance between A and B.
Work is done in moving the negative charge from point A to point B.
If the electric flux through a closed surface is zero, the electric field at points on that surface must be zero.
True
False
The figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have an electric flux of +q/ε0 through them?
a
b
c
d
The figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have no electric flux through them?
a
b
c
d
Which of the following statements about Gauss's law are correct? (There may be more than one correct choice.)
Gauss's law is valid only for symmetric charge distributions, such as spheres and cylinders.
If there is no charge inside of a Gaussian surface, the electric field must be zero at points of that surface.
Only charge enclosed within a Gaussian surface can produce an electric field at points on that surface.
If a Gaussian surface is completely inside an electrostatic conductor, the electric field must always be zero at all points on that surface.
The electric flux passing through a Gaussian surface depends only on the amount of charge inside that surface, not on its size or shape.
Consider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside the sphere. To maximize the magnitude of the flux of the electric field through the Gaussian surface, the charge should be located
at x = 0, y = 0, z = R/2.
at x = R/2, y = 0, z = 0.
at the origin.
at x = 0, y = R/2, z = 0.
The charge can be located anywhere, since flux does not depend on the position of the charge as long as it is inside the sphere.
The graph in the figure shows the electric field strength (not the field lines) as a function of distance from the center for a pair of concentric uniformly charged spheres. Which of the following situations could the graph plausibly represent? (There may be more than one correct choice.)
a positively charged conducting sphere within another positively charged conducting sphere
a positively charged conducting sphere within an uncharged conducting sphere
a solid nonconducting sphere, uniformly charged throughout its volume, inside of a positively charged conducting sphere
a positively charged nonconducting thin-walled spherical shell inside of a positively charged conducting sphere
a positively charged nonconducting thin-walled spherical shell inside of another positively charged nonconducting thin-walled spherical shell
Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is
along a line between the lines closer to line #2 than line #1.
at a point midway between the lines.
along a line perpendicular to lines #1 and #2.
along a line between the lines closer to line #1 than line #2.
At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?
2D
√2*D
D / √2
D/2
D/4
An uncharged conductor has a hollow cavity inside of it. Within this cavity there is a charge of +10 µC that does not touch the conductor. There are no other charges in the vicinity. Which statement about this conductor is true? (There may be more than one correct choice.)
The inner surface of the conductor carries a charge of -10 µC and its outer surface carries no excess charge.
The inner and outer surfaces of the conductor each contain charges of -5 µC.
The net electric field within the material of the conductor points away from the +10 µC charge.
The outer surface of the conductor contains +10 µC of charge and the inner surface contains - 10 µC.
Both surfaces of the conductor carry no excess charge because the conductor is uncharged.
Under electrostatic conditions, the electric field just outside the surface of any charged conductor
is always parallel to the surface.
is always zero because the electric field is zero inside conductors.
is always perpendicular to the surface of the conductor.
is perpendicular to the surface of the conductor only if it is a sphere, a cylinder, or a flat sheet.
can have nonzero components perpendicular to and parallel to the surface of the conductor.
The figure shows two unequal point charges, q and Q, of opposite sign. Charge Q has greater magnitude than charge q. In which of the regions X, Y, Z will there be a point at which the net electric field due to these two charges is zero?
only regions X and Z
only region X
only region Y
only region Z
all three regions
Two point charges Q1 and Q2 of equal magnitudes and opposite signs are positioned as shown in the figure. Which of the arrows best represents the net electric field at point P due to these two charges?
A
B
C
D
The field is equal to zero at point P.
Three equal negative point charges are placed at three of the corners of a square of side d as shown in the figure. Which of the arrows represents the direction of the net electric field at the center of the square?
A
B
C
D
The field is equal to zero at point P.
The figure shows three electric charges labeled Q1, Q2, Q3, and some electric field lines in the region surrounding the charges. What are the signs of the three charges?
Q1 is positive, Q2 is negative, Q3 is positive.
Q1 is negative, Q2 is positive, Q3 is negative.
Q1 is positive, Q2 is positive, Q3 is negative.
All three charges are negative.
All three charges are positive.
Two very large parallel sheets a distance d apart have their centers directly opposite each other. The sheets carry equal but opposite uniform surface charge densities. A point charge that is placed near the middle of the sheets a distance d/2 from each of them feels an electrical force F due to the sheets. If this charge is now moved closer to one of the sheets so that it is a distance d/4 from that sheet, what force will feel?
4F
2F
F
F/2
F/4
An electron is initially moving to the right when it enters a uniform electric field directed upwards. Which trajectory shown below will the electron follow?
trajectory W
trajectory X
trajectory Y
trajectory Z
Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually leaks off of both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be
1/16 F.
1/8 F.
1/4 F.
1/2 F.
When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F. In order to make this force twice as strong, the distance would have to be changed to
2d.
√2*d.
d / √2 .
d/2.
d/4.
A point charge Q is located a short distance from a point charge 3Q, and no other charges are present. If the electrical force on Q is F, what is the electrical force on 3Q?
F/3
√3 * F
F / √3
F
3F
A positive point charge Q is fixed on a very large horizontal frictionless tabletop. A second positive point charge q is released from rest near the stationary charge and is free to move. Which statement best describes the motion of q after it is released?
Its speed will be greatest just after it is released.
Its acceleration is zero just after it is released.
As it moves farther and farther from Q, its acceleration will keep increasing.
As it moves farther and farther from Q, its speed will decrease.
As it moves farther and farther from Q, its speed will keep increasing.
One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the distance between the balls in the test tube would become
2d
√2 * d
4d
8d
The grey circle must have a charge that is
positive
negative
neutral
not enough information given
The point with the highest electric potential is
A
B
D
None of the above
The point with the largest magnitude of electric field is ______
A
B
D
None of the above
In order to move an electron from A to D, it would require
positive work
negative work
zero work
None of the above
At point P, the electrical potential is
positive
negative
zero
points to the left
At point P, the electric field
points left
points right
is zero
is negative
If an electron were placed at point P, it would a experience
force to the right
force to the left
no net force
At point P, the net potential is
positve
negative
zero
If a proton were placed at point P, it would
stay at rest
accelerate to the left
accelerate to the right
At the origin, the potential is
positive
negative
zero
At which is the electric field the greatest?
B
D
E
F
