AP Physics E/M Final Review

A. (1/3) uF B. (2/3) uF C. 2 uF D. 3 uF E. 9 uF

(1/3) uF

Two charges, -2Q and +Q, are located on the x-axis, as shown right. Point P, at a distance of 3D from the origin 0, is one of two points on the positive x-axis at which the electric potential is zero. How far from the origin 0 is the other point? A. (2D)/3 B. D C. (3D)/2 D. (5D)/3 E. 2D

(5D)/3

Two concentric, spherical conducting shells have radii r1 and r2 and charges Q1 and Q2, as shown right. Let r be the distance from the center of the spheres and consider the region r1 < r < r2. In this region the electric potential relative to infinity is proportional to A. Q1/r² B. (Q1+Q2)/r² C. (Q1+Q2)/r D. (Q1/r1) + (Q2/r2) E. (Q1/r) + (Q2/r2)

(Q1/r) + (Q2/r2)

As shown in the diagram left, a charged particle having a mass m and charge -q is projected into the region between two parallel plates with a speed v0 to the right. The potential difference between the plates is V and they are separated by a distance d. What is the net change in kinetic energy of the particle during the time it takes the particle to transverse the distance d? A. +1/2 mv0² B. -q(V/d) C. +2q(V/mv0²) D. +qV E. -qd/V

+qV

The electric field of two long coaxial cylinders is represented by lines of force as shown left. The charge on the inner cylinder is +Q. The charge on the outer cylinder is A. +3Q B. +Q C. zero D. -Q E. -3Q

-3Q

A. 8 V B. 6 V C. 4 V D. 2 V E. 0 V

0 V

A. 1 A B. 2 A C. 3 A D. 4 A E. 12.8 A

1 A

A. 1 ohm in series with it B. 901 ohms in series with it C. 9900 ohms in series with it D. 1 ohm in parallel with it E. 9900 ohms in parallel with it

1 ohm in parallel with it

A. 1 to 4 B. 1 to 2 C. 1 to 1 D. 2 to 1 E. 4 to 1

1 to 2

A. 1/2 B. 1/(2)^1/2 C. 1 D. (2)^1/2 E. 2

1/2

A. 10 amps B. 14.1 amps C. 18 amps D. 20 amps E. 36 amps

10 amps

A. 10.5 V B. 10.8 V C. 11.6 V D. 12.0 V E. 13.0 V

10.8 V

a. 10^-2 ohm B. 10^-1 ohm C. 1 ohm D. 10 ohm E. 100 ohms

100 ohms

A. 3.4 V B. 4 V C. 12 V D. 16 V E. 24 V

12 V

A. 4 uJ B. 6 uJ C. 12 uJ D. 18 uJ E. 36 uJ

12 uJ

A. 4 V B. 8 V C. 10 V D. 12 V E. 16 V

16 V

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 A. F B. 2F C. 4F D. 8F E. 16F

16F

A. .5 uF B. 2 uF C. 3 uF D. 9 uF E. 18 uF

2 uF

A. 2 x 10^-6 ohm B. 1 x 10^-3 ohm C. 2 x 10^-3 ohm D. 20 ohm E. 2 x 10^3 ohm

2 x 10^-3 ohm

Four positive charges of magnitude q are arranged at the corners of a square, as shown right. At the center C of the square, the potential due to one charge alone is V0 and the electric field due to one charge alone has magnitude E0. Which of the following correctly gives the electric potential and the magnitude of the electric field at the center of the square due to all four charges? A. V=0 and E=0 B. V=0 and E=2E0 C. V=2V0 and E=4E0 D. V=4V0 and E=0 E. V=4V0 and E=2E0

V=4V0 and E=0

The potential of an isolated conducting sphere of radius R is given as a function of the charge q on the sphere by the equation V=kq/R. If the sphere is initially uncharged, the work W required to gradually increase the total charge on the sphere from zero to Q is given by which of the following expressions? A. W=(kQ)/R B. W=(kQ²)/R C. W=f0^Q(kq)Rdq D. W=f0^Q(kq²)/Rdq E. W=f0^Q(kq)/R²dq

W=f0^Q(kq)/Rdq

A point charge is placed at the center of an uncharged, spherical, conducting shell of radius R. The electric fields inside and outside the sphere are measured. The point charge is then moved off center a distance R/2 and the fields are measured again. What is the effect on the electric fields? A. changed neither inside nor outside B. changed inside, but not changed outside C. not changed inside, but changed outside D. changed inside and outside E. it cannot be determined without further information

changed inside, but not changed outside

The electric field E just outside the surface of a charged conductor is A. directed perpendicular to the surface B. directed parallel to the surface C. independent of the surface charge density D. zero E. infinite

directed perpendicular to the surface

A. l only B. d only C. l and p only D. d and p only E. l, d, and p

l and p only

Two conducting spheres, one having twice the diameter of the other, are shown left. The smaller sphere initially has a charge +q. When the spheres are connected by a thin wire, which of the following is true? A. one and two are both at the same potential B. two has twice the potential of one C. two has half the potential of one D. one and two have equal charges E. all of the charge is dissipated

one and two are both at the same potential

A charged particle traveling with a velocity v in an electric field E experiences a force F that must be A. parallel to v B. perpendicular to v C. parallel to v x E D. parallel to E E. perpendicular to E

parallel to E

Two metal spheres that are initially uncharged are mounted on insulating stands, as shown left. 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? A. zero (sphere X), zero (sphere Y) B. negative (sphere X), negative (sphere Y) C. negative (sphere X), positive (sphere Y) D. positive (sphere X), negative (sphere Y) E. positive (sphere X), positive (sphere Y)

positive (sphere X), negative (sphere Y)

A distribution of charge is confined to a finite region of space. The difference in electric potential between any two points P1 and P2 due to this charge distribution depends only upon the A. charges located at the point P1 and P2 B. magnitude of a test charge moved from P1 to P2 C. value of the electric field at P1 and P2 D. path taken by a test charge moved from P1 to P2 E. value of the integral of -∫E•dr

value of the integral of -∫E•dr

A positive charge +Q located at the origin produces an electric field E0 at point P (x = +1, y = 0). A negative charge -2Q is placed at such a point as to produce a net field of zero at point P. The second charge will be placed on the A. x-axis where x>1 B. x-axis where 0<x<1 C. x-axis where x<0 D. y-axis where y>0 E. y-axis where y<0

x-axis where x<0

A charge of +12 units is located in the xy plane of a coordinate system at (+3,0) and a second charge of +6 units is located at (-3,0) as shown left. Where on the x-axis should an additional charge of +24 units be located to produce an electric field equal to zero at the origin (0,0)? A. x=-6 B. x=2 C. x=+1 D. x=+2 E. x=+6

x=-6

A closed surface, in the shape of a cube of side a, is oriented as shown left in a region where there is a constant electric field of magnitude E parallel to the x-axis. The total electric flux through the cubical surface is A. -Ea² B. zero C. Ea² D. 2Ea² E. 6Ea²

zero

The net electric flux through a closed surface is A. infinite only if there are no charges enclosed by the surface B. infinite only if the net charge enclosed by the surface is zero C. zero if only negative charges are enclosed by the surface D. zero if only positive charges are enclosed by the surface E. zero if the net charge enclosed by the surface is zero

zero if the net charge enclosed by the surface is zero

A conducting sphere of radius R carries a charge Q. Another conducting sphere has a radius R/2, but carries the same charge. The spheres are far apart. The ratio of the electric field near the surface of the smaller sphere to the field near the surface of the larger sphere is most nearly A. 1/4 B. 1/2 C. 1 D. 2 E. 4

4

A. 1 ohm b. 2 ohms C. 4 ohms D. 20 ohms E. 24 ohms

4 ohms

A. 3 ohms B. 4 ohms C. 6 ohms D. 12 ohms E. 18 ohms

4 ohms

A. 0.22 ohms B. 4.5 ohms C. 5 ohms D. 16 ohms E. 70 ohms

5 ohms

A. 1.5 V B. 3 V C. 6 V D. 9 V E. 18 V

6 V

A positive charge of 3.0 x 10^-8 coulomb is placed in an upward-directed uniform electric field of 4.0 x 10^4 newtons per coulomb. When the charge is moved .5 meter upward, the work done by the electric force on the charge is A. 6 x 10^-4 J B. 12 x 10^-4 J C. 2 x 10^4 J D. 8 x 10^4 J E. 12 x 10^4 J

6 x 10^-4 J

A conducting sphere with a radius of .1 meter has 1.0 x 10^-9 coulomb of charge deposited on it. The electric field just outside the surface of the sphere is A. zero B. 450 V/m C. 900 V/m D. 4500 V/m E. 900000 V/m

900 V/m

A. (1/4)C0 B. (1/2)C0 C. C0 D. 2C0 E. 4C0

C0

A. Potential difference between the two ends B. Electric field strength within the resistor C. Resistance D. Current per unit area E. Current

Current

A solid nonconducting sphere of radius R has a charge Q uniformly distributed throughout its volume. A Gaussian surface of radius r with r < R is used to calculate the magnitude of the electric field E at a distance r from the center of the sphere. Which of the following equations results from a correct application of Gauss's law for this situation? A. E(4πR²)=Q/ε0 B. E(4πr²)=Q/ε0 C. E(4πr²)=(Q/ε0)E(3r³/4πR²) D. E(4πr²)=(Q/ε0)(r³/R³) E. E(4πr²)=0

E(4πr²)=(Q/ε0)(r³/R³)

Refer to a sphere of radius R that has a positive charge Q uniformly distributed on its surface. Which of the following represents the magnitude of the electric field E and the potential V as functions of r, the distance from the center of the sphere, when r < R? A. E=0 and V =kQ/R B. E=0 and V=kQ/r C. E=0 and V=0 D. E=kQ/r² and V=0 E. E=kQ/R² and V=0

E=0 and V=kQ/R

Refer to a sphere of radius R that has a positive charge Q uniformly distributed on its surface. Which of the following represents the magnitude of the electric field E and the potential V as functions of r, the distance from the center of the sphere, when r > R? A. E=kQ/R² and V=KQ/R B. E=kQ/R and V=kQ/R C. E=kQ/R and V=KQ/r D. E=kQ/r² and V=kQ/r E. E=kQ/r² and V=kQ/r²

E=kQ/r² and V=kQ/r

Two identical conducting spheres are charged to +2Q and -Q respectively, and are separated by a distance d (much greater than the radii of the spheres). The magnitude of the force of attraction on the left sphere is F1. After the two spheres are made to touch and then are re-separated by distance d, the magnitude of the force on the left sphere is F2. Which of the following relationships is correct? A. 2F1=F2 B. f1=F2 C. F1=2F2 D. F1=4F1 E. F1=8F2

F1=8F2

Two conducting spheres, X and Y, have the same positive charge +Q, but different radii (rx > ry) as shown right. The spheres are separated so that the distance between them is large compared with either radius. If a wire is connected between them, in which direction will current be directed in the wire? A. From X to Y B. From Y to X C. There will be no current in the wire. D. It cannot be determined without knowing the magnitude of Q. E. It cannot be determined without knowing whether the spheres are solid or hollow.

From Y to X

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 II. The magnitude of the electrostatic force exerted per unit charge on a test charge at that point III. The electrostatic charge at that point A. I only B. III only C. I and II only D. II and III only E. I, II, and III

I and II only

A. It depends on the charge on each capacitor. B. It depends on the potential difference across both capacitors. C. It is larger than the capacitance of each capacitor. D. It is smaller than the capacitance of each capacitor. E. It is the same as the capacitance of each capacitor.

It is smaller than the capacitance of each capacitor.

A. Placing another capacitor in parallel with C B. Placing another capacitor in series with C C. Placing another resistor in parallel with the resistor R D. Increasing battery Emf E. Decreasing battery Emf

Placing another capacitor in parallel with C

Two concentric, spherical conducting shells have radii r1 and r2 and charges Q1 and Q2, as shown right. Let r be the distance from the center of the spheres and consider the region r1 < r < r2. In this region the electric field is proportional to A. Q1/r² B. (Q1+Q2)/r² C. (Q1+Q2)/r D. (Q1/r1) + (Q2/r2) E. (Q1/r) + (Q2/r2)

Q1/r²

A. Q=Q0 and V>V0 B. Q=Q0 and V<V0 C. Q>Q0 and V=V0 D. Q<Q0 and V<V0 E. Q>Q0 and V>V0

Q=Q0 and V<V0

A. The capacitance of the capacitor. B. The total charge on the capacitor. C. The surface density of the charge on the plates of the capacitor. D. The energy stored in the capacitor. E. The intensity of the electric field between the plates of the capacitor.

The energy stored in the capacitor.

The point charge Q shown right is at the center of a metal box that is isolated, undergrounded, and uncharged. Which of the following is true? A. The net charge on the outside surface of the box is Q. B. The potential inside the box is zero. C. The electric field inside the box is constant. D. The electric field outside the box is zero everywhere. E. The electric field outside the box is the same as if only the point charge (and not the box) were there.

The net charge on the outside surface of the box is Q.

A. The capacitance decreases. B. The potential difference across the capacitor decreases. C. The energy of the capacitor does not change. D. The charge of the capacitor plates decreases. E. The electric field between the capacitor plates increases.

The potential difference across the capacitor decreases.

Which of the following can be used along with fundamental constants, but not other quantities, to calculate the magnitude of the electric field E between the plates of a parallel-place capacitor whose plate dimensions and spacing are not known? A. The flux between the plates B. The total charge on either plate C. The potential difference between the plates D. The surface charge density on either plate E. The total energy stored in the capacitor

The surface charge density on either plate

Which of the following statements about conductors under electrostatic conditions is true? A. Positive work is required to move a positive charge over the surface of a conductor. B. Charge that is placed on the surface of a conductor always spreads evenly over the surface. C. The electric potential inside a conductor is always zero. D. The electric field at the surface of a conductor is tangent to the surface. E. The surface of a conductor is always an equipotential surface.

The surface of a conductor is always an equipotential surface.

A circular ring made of an insulating material is cut in half. One half is given a charge -q uniformly distributed along its arc. The other half is given a charge +q also uniformly distributed along its arc. The two halves are then rejoined with insulation at the junctions J, as shown left. If there is no change in the charge distributions, what is the direction of the net electrostatic force on an electron located at the center of the circle? A. Toward the top of the page B. Toward the bottom of the page C. To the right D. To the left E. Into the page

Toward the bottom of the page

Positive charge Q is uniformly distributed over a thin ring of radius a that lies in a plane perpendicular to the x-axis, with its center at the origin 0, as shown right. The potential V at points on the x-axis is represented by which of the following functions? A. V(x) = (kQ)/(a²+x²) B. V(x) = (kQ)/(a²+x²)^1/2 C. V(x) = kQ/x² D. V(x) = kQ/x E. V(x) = (kQ)/(a+x)

V(x) = (kQ)/(a²+x²)^1/2

What is the radial component of the electric field associated with the potential V=ar^-2, where a is a constant? A. -2ar^-3 B. -2ar^-1 C. ar^-1 D. 2ar^-1 E. 2ar^-3

2ar^-3

A. 0 B. r/2 C. r D. 2r E. 4r

2r

A. (2/3) uF B. (4/3) uF C. 3 uF D. 6 uF E. 12 uF

3 uF