Two identical conducting spheres are charged to +2Q and -Q respectively and are separated by a distance d. The magnitude of the force of attraction on the left sphere is F₁. After the two spheres are made to touch and then are reseparated by distance d the magnitude of the force on the left sphere is F₂. Which relationship is correct?

E) F₁ = 8F₂

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

E) 16F

A charged particle traveling with a velocity v in an electric field E experiences a force F that must be

D) parallel to E

In which configuration is the electric field at P equal to zero? (Three charges at vertices of equilateral triangle P equidistant from charges)

A) Configuration A

In which configuration is the electric field at P pointed at the midpoint between two of the charges?

C) Configuration C

Positive charge Q is uniformly distributed over a thin ring of radius a perpendicular to the x-axis with center at origin. Which graph best represents the electric field along the positive x-axis?

B) Graph B (field zero at center increases then decreases)

From the electric field vector at a point one can determine which of the following? I. Direction of electrostatic force on test charge of known sign II. Magnitude of electrostatic force per unit charge III. The electrostatic charge at that point

C) I and II only

A circular ring made of insulating material is cut in half. One half carries charge -q the other +q uniformly distributed. The two halves are rejoined with insulation at junctions. What is the direction of the net electrostatic force on an electron at the center?

A) Toward the top of the page

A conducting sphere of radius R carries charge Q. Another conducting sphere has 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

E) 4

Two metal spheres on insulating stands are initially uncharged. A negatively charged rubber rod is brought close to but does not touch sphere X. Sphere Y is then brought close to X on the side opposite to the rod. Y touches X then is removed. The rod is moved far away. What are the final charges on the spheres?

D) Sphere X: Positive Sphere Y: Negative

Two initially uncharged conductors 1 and 2 are mounted on insulating stands in contact. A negatively charged rod is brought near but does not touch them. With the rod held in place conductor 2 is moved away. Which is now true of conductor 2?

B) It is positively charged

Two particles each of charge +Q are fixed at opposite corners of a square. A positive test charge +q is placed at a third corner. What is the direction of the force on the test charge?

E) Direction shown in diagram

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 charges?

D) √2 F

If the only force acting on an electron is due to a uniform electric field the electron moves with constant

A) acceleration in a direction opposite to that of the field

Two charged particles each with charge +q are located along the x-axis at x = 2 and x = 4. Which graph shows the magnitude of the electric field along the x-axis from origin to x = 6?

A) Graph showing peaks at x=2 and x=4 zero at x=3

Particles of charge Q and -4Q are on the x-axis. Which describes the direction of the electric field at point P?

E) Components in both the +x- and -y-directions

At which labeled point on the x-axis is the electric field zero? (Q at origin -4Q to the right)

A) Point A

When a negatively charged rod is brought near an initially uncharged electroscope the leaves spring apart (I). When touched with a finger they collapse (II). When finger and rod are removed leaves spring apart again (III). The charge on the leaves is

D) negative in I positive in III

Two infinite parallel sheets of charge perpendicular to the x-axis have equal and opposite charge densities. Which graph best represents electric field as a function of x?

E) Constant between plates zero outside

A point charge is placed at the center of an uncharged spherical conducting shell of radius R. The point charge is then moved off center a distance R/2. What is the effect on the electric fields?

B) 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

A closed cube of side a is oriented in a region where there is a constant electric field E parallel to the x-axis. The total electric flux through the cubical surface is

B) zero

A spherical distribution of charge of radius R has constant charge density ρ. Which graph best represents the electric field strength E as a function of distance r from the center?

A) Linear inside 1/r² outside

The electric field of two long coaxial cylinders shows lines of force. The inner cylinder has charge +Q. The charge on the outer cylinder is

E) -3Q

The net electric flux through a closed surface is

E) zero if the net charge enclosed by the surface is zero

A solid nonconducting sphere of radius R has charge Q uniformly distributed. A Gaussian surface of radius r < R is used to calculate the electric field. Which equation results from correct application of Gauss's law?

D) E(4πr²) = (Qr³)/(ε₀R³)

A point charge Q is at the center of a metal box that is isolated ungrounded and uncharged. Which is true?

A) The net charge on the outside surface of the box is Q

Gauss's law provides a convenient way to calculate the electric field outside and near each of the following isolated charged conductors EXCEPT a

C) cube

A point charge +Q is inside an uncharged conducting spherical shell that is near several isolated point charges. The electric field at point P inside the shell depends on the magnitude of

A) Q only

A uniform spherical charge distribution has radius R. Which is true of the electric field strength due to this charge distribution at distance r from center?

D) It is directly proportional to r when r < R

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

E) value of the integral -∫E·dr from P₁ to P₂

Two small spheres having charges of +2Q and -Q are 12 cm apart. The potential of points on a line joining the charges is best represented as a function of distance x from the positive charge by which graph?

D) Graph D

In which configuration are both the electric field and the electric potential at the origin equal to zero?

E) Configuration E

In which configuration is the value of the electric field at the origin equal to zero but the electric potential at the origin not equal to zero?

B) Configuration B

Two infinite parallel sheets of charge with equal and opposite densities. Which graph best represents electric potential as a function of x?

B) Linear between plates constant outside

An insulated spherical conductor of radius r₀ carries charge q. The electric potential due to this system varies as a function of distance r from the center in which way?

A) Constant inside 1/r outside

A charged particle having mass m and charge -q is projected into the region between two parallel plates with speed v₀. The potential difference is V and plate separation is d. What is the net change in kinetic energy during time to traverse distance d?

D) +qV

Two conducting spheres one having twice the diameter of the other. The smaller sphere initially has charge +q. When the spheres are connected by a thin wire which is true?

A) 1 and 2 are both at the same potential

Points R and S are each the same distance d from two unequal charges +Q and +2Q. The work required to move charge -Q from point R to point S is

D) zero

Two positive charges of magnitude q are each a distance d from the origin A. At which point is the electric potential greatest in magnitude?

A) Point A

Concentric conducting spheres of radii a and 2a bear equal but opposite charges +Q and -Q. Which graph best represents the electric potential V as a function of r?

D) Graph D

Which statement about conductors under electrostatic conditions is true?

E) The surface of a conductor is always an equipotential surface

A positive charge of 3.0 × 10⁻⁸ coulomb is in an upward directed uniform electric field of 4.0 × 10⁴ N/C. When the charge is moved 0.5 meter upward the work done by the electric force is

A) 6 × 10⁻⁴ J

Two conducting spheres X and Y have the same positive charge +Q but different radii (rₓ > rᵧ). If a wire is connected between them in which direction will current be directed?

B) From Y to X

A sphere of radius R has positive charge Q uniformly distributed on its surface. Which represents the magnitude of the electric field E and potential V as functions of r when r < R?

A) E=0 V=kQ/R

Which represents the magnitude of electric field E and potential V as functions of r when r > R?

D) E=kQ/r² V=kQ/r

Positive charge Q is uniformly distributed over a thin ring of radius a perpendicular to the x-axis with center at origin. The potential V at points on the x-axis is represented by which function?

B) V(x) = kQ/√(a²+x²)

Four positive charges of magnitude q are at the corners of a square. At center C the potential due to one charge alone is V₀ and electric field due to one charge alone has magnitude E₀. Which correctly gives the electric potential and magnitude of electric field at center due to all four charges?

D) Electric Potential: 4V₀ Electric Field: Zero

Two charges -2Q and +Q are on the x-axis. Point P at distance 3D from origin is one of two points on positive x-axis where electric potential is zero. How far from origin O is the other point?

D) 5/3 D

What is the radial component of the electric field associated with the potential V = ar⁻² where a is a constant?

E) 2ar⁻³

Two concentric spherical conducting shells have radii r₁ and r₂ and charges Q₁ and Q₂. In the region r₁ < r < r₂ the electric field is proportional to

A) Q₁/r²

In this region the electric potential relative to infinity is proportional to

E) Q₁/r + Q₂/r²

A battery connected to two parallel plates produces equipotential lines between the plates. Which configuration is most likely to produce these equipotential lines?

D) Configuration D

The force on an electron located on the 0-volt potential line is

D) directed to the right but its magnitude cannot be determined without knowing the distance between the lines

The potential of an isolated conducting sphere of radius R is given as V = kq/R. If the sphere is initially uncharged the work W required to gradually increase the total charge from zero to Q is

C) W = ∫₀Q (kq/R)dq

Two charges +3q and +2q are located on a line. Other than at infinity the electric field strength is zero at a point on the line in which range?

C) Between II and III

The electric potential is negative at some points on the line in which ranges?

E) None; this potential is never negative

The graph shows electric potential V as a function of position along the x-axis. At which point would a charged particle experience the force of greatest magnitude?

D) Point D

The work that must be done by an external agent to move a point charge of 2 mC from the origin to a point 3 m away is 5 J. What is the potential difference between the two points?

C) 2.5 × 10³ V

An electron (charge -e) could orbit a proton (charge +e) in a circular orbit of constant radius R. Assuming the proton is stationary and only electrostatic forces act which represents the kinetic energy of the two-particle system?

B) (1/8πε₀)(e²/R)

In a region of space a spherically symmetric electric potential is given by V(r) = kr². What is the magnitude of the electric field at a point a distance r₀ from the origin?

C) 2kr₀

What is the direction of the electric field at distance r₀ from origin and direction of force on an electron placed at this point?

C) Electric Field: Away from origin Force on Electron: Toward origin

A positive electric charge is moved at constant speed between two locations in an electric field with no work done by or against the field. This situation can occur only if the

D) charge is moved along an equipotential line

A nonconducting hollow sphere of radius R carries charge +Q uniformly distributed on its surface. A small charge +q is initially at point P distance r from center. What is the work done by an external agent in moving charge +q from P through the hole to center O?

E) kqQ(1/R - 1/r)

In a certain region the electric field along the x-axis is E = ax + b where a = 40 V/m² and b = 4 V/m. The potential difference between the origin and x = 0.5 m is

B) -7 V

A 20 μF parallel-plate capacitor is fully charged to 30 V. The energy stored in the capacitor is most nearly

B) 9 × 10⁻³ J

A potential difference V is maintained between two large parallel conducting plates. An electron starts from rest on the surface of one plate and accelerates toward the other. Its speed as it reaches the second plate is proportional to

D) √V

A solid metallic sphere of radius R has charge Q uniformly distributed on its outer surface. Which graph best represents the magnitude of the electric field E as a function of position r for this sphere?

C) Zero inside 1/r² outside

Six particles each with charge +Q are held fixed and equally spaced around the circumference of a circle of radius R. What is the magnitude of the resultant electric field at the center of the circle?

A) 0

With the six particles held fixed how much work would be required to bring a seventh particle of charge +Q from very far away and place it at the center of the circle?

D) (6Q²)/(4πε₀R)

The diagram shows equipotential lines produced by an unknown charge distribution. Which vector best describes the direction of the electric field at point A?

A) Downward direction

At which point does the electric field have the greatest magnitude?

B) Point B

How much net work must be done by an external force to move a -1 μC point charge from rest at point C to rest at point E?

B) -10 μJ

A physics problem starts: 'A solid sphere has charge distributed uniformly throughout...' It may be correctly concluded that the

E) sphere is not made of metal