AP Physics C Capacitance Flashcards

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 points 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 -∫E·dr from P1 to P2

Two small spheres having charges of +2Q and -Q are 12 centimeters apart. The potential of points lying on a line joining the charges is best represented as a function of the distance x from the positive charge by which of the following? (A) Graph A (B) Graph B (C) Graph C (D) Graph D (E) Graph E

In which configuration are both the electric field and the electric potential at the origin equal to zero? Five charge configurations on xy-plane using two or four point charges. (A) A (B) B (C) C (D) D (E) 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? (A) A (B) B (C) C (D) D (E) E

Two infinite parallel sheets of charge perpendicular to the x-axis have equal and opposite charge densities as shown above. Which graph best represents the plot of electric potential as a function of x? (A) Graph A (B) Graph B (C) Graph C (D) Graph D (E) Graph E

An insulated spherical conductor of radius ro carries a charge q. The electric potential due to this system varies as a function of the distance r from the center of the sphere in which of the following ways? The potential is taken to be zero at r = ∞. (A) Graph A (B) Graph B (C) Graph C (D) Graph D (E) Graph E

As shown in the diagram above a charged particle having mass m and charge -q is projected into the region between two parallel plates with a speed vo 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 traverse the distance d? (A) +½mvo² (B) -qV/d (C) +qV/d (D) +qV (E) None of the above

Two conducting spheres one having twice the diameter of the other are shown above. The smaller sphere initially has a charge +q. When the spheres are connected by a thin wire which of the following is true? (A) 1 and 2 are both at the same potential (B) 2 has twice the potential of 1 (C) 2 has half the potential of 1 (D) 1 and 2 have equal charges (E) All of the charge is dissipated

Points R and S are each the same distance d from two unequal charges +Q and +2Q as shown above. The work required to move a charge -Q from point R to point S is (A) dependent on the path taken from R to S (B) directly proportional to the distance between R and S (C) positive (D) zero (E) negative

Two positive charges of magnitude q are each a distance d from the origin A of a coordinate system as shown above. At which of the following points is the electric potential greatest in magnitude? (A) A (B) B (C) C (D) D (E) E

Concentric conducting spheres of radii a and 2a bear equal but opposite charges +Q and -Q respectively. Which of the following graphs best represents the electric potential V as a function of r? (A) Graph A (B) Graph B (C) Graph C (D) Graph D (E) Graph E

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

A positive charge of 3.0 × 10⁻⁸ coulomb is placed 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 on the charge is (A) 6 × 10⁻⁴ J (B) 12 × 10⁻⁴ J (C) 2 × 10⁴ J (D) 8 × 10⁴ J (E) 12 × 10⁴ J

Two conducting spheres X and Y have the same positive charge +Q but different radii (rx > ry) as shown above. 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

A sphere of radius R has 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 V: kQ/R (B) E: 0 V: kQ/r (C) E: 0 V: 0 (D) E: kQ/r² V: 0 (E) E: kQ/R² V: 0

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 sphere when r > R? (A) E: kQ/R² V: kQ/R (B) E: kQ/R V: kQ/R (C) E: kQ/R V: kQ/r (D) E: kQ/r² V: kQ/r (E) E: kQ/r² V: kQ/r²

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 O as shown above. The potential V at points on the x-axis is represented by which of the following functions? (A) V(x) = kQ/√(x²+a²) (B) V(x) = kQ/√(a²+x²) (C) V(x) = kQ/x² (D) V(x) = kQ/x (E) V(x) = kQ/(x+a)

Four positive charges of magnitude q are arranged at the corners of a square as shown above. At the center C of the square the potential due to one charge alone is Vo and the electric field due to one charge alone has magnitude Eo. 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) Electric Potential: Zero Electric Field: Zero (B) Electric Potential: Zero Electric Field: 2Eo (C) Electric Potential: 2Vo Electric Field: 4Eo (D) Electric Potential: 4Vo Electric Field: Zero (E) Electric Potential: 4Vo Electric Field: 2Eo

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

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

Two concentric spherical conducting shells have radii r1 and r2 and charges Q1 and Q2 as shown above. 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/r (E) Q1/r+Q2/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/r (E) Q1/r+Q2/r²

A battery or batteries connected to two parallel plates produce the equipotential lines between the plates shown above. Which of the following configurations is most likely to produce these equipotential lines? (A) Config A (B) Config B (C) Config C (D) Config D (E) Config E

The force on an electron located on the 0-volt potential line is (A) 0 N (B) 1 N directed to the right (C) 1 N directed to the left (D) directed to the right but its magnitude cannot be determined without knowing the distance between the lines (E) directed to the left 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 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 = ∫(kq/R)dq from 0 to Q (D) W = ∫(kq/R)dq from 0 to Q² (E) W = ∫(kq²/R)dq from 0 to Q

Two charges located on a line where charge at point I is +3q and charge at point III is +2q. Point II is halfway between points I and III. Other than at infinity the electric field strength is zero at a point on the line in which of the following ranges? (A) To the left of I (B) Between I and II (C) Between II and III (D) To the right of III (E) None; the field is zero only at infinity

The electric potential is negative at some points on the line in which of the following ranges? (A) To the left of I (B) Between I and II (C) Between II and III (D) To the right of III (E) None; this potential is never negative

The graph above shows the electric potential V in a region of space as a function of position along the x-axis. At which point would a charged particle experience the force of greatest magnitude? (A) A (B) B (C) C (D) D (E) E

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? (A) 4 × 10⁻⁴ V (B) 10⁻² V (C) 2.5 × 10³ V (D) 2 × 10⁶ V (E) 6 × 10⁶ V

Suppose that an electron (charge -e) could orbit a proton (charge +e) in a circular orbit of constant radius R. Assuming that the proton is stationary and only electrostatic forces act on the particles which of the following represents the kinetic energy of the two-particle system? (A) (1/4πεo)(e/R) (B) (1/8πεo)(e²/R) (C) -(1/8πεo)(e²/R) (D) (1/4πεo)(e²/R²) (E) -(1/4πεo)(e²/R²)

In a region of space a spherically symmetric electric potential is given as a function of r the distance from the origin by the equation V(r) = kr² where k is a positive constant. What is the magnitude of the electric field at a point a distance ro from the origin? (A) Zero (B) kro (C) 2kro (D) kro² (E) 2kro³/3

What is the direction of the electric field at a point a distance ro from the origin and the direction of the force on an electron placed at this point? (A) Electric Field: Toward origin Force on Electron: Toward origin (B) Electric Field: Toward origin Force on Electron: Away from origin (C) Electric Field: Away from origin Force on Electron: Toward origin (D) Electric Field: Away from origin Force on Electron: Away from origin (E) Electric Field: Undefined since the field is zero Force on Electron: Undefined since the force is zero

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 (A) charge is moved in the direction of the field (B) charge is moved opposite to the direction of the field (C) charge is moved perpendicular to an equipotential line (D) charge is moved along an equipotential line (E) electric field is uniform

The nonconducting hollow sphere of radius R shown above carries a large charge +Q which is uniformly distributed on its surface. There is a small hole in the sphere. A small charge +q is initially located at point P a distance r from the center of the sphere. If k = 1/4πεo what is the work that must be done by an external agent in moving the charge +q from P through the hole to the center O of the sphere? (A) Zero (B) kqQ/r (C) kqQ/R (D) kq(Q-q)/r (E) kqQ(1/R-1/r)

In a certain region the electric field along the x-axis is given by 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 (A) -36 V (B) -7 V (C) -3 V (D) 10 V (E) 16 V

A 20 μF parallel-plate capacitor is fully charged to 30 V. The energy stored in the capacitor is most nearly (A) 9 × 10³ J (B) 9 × 10⁻³ J (C) 6 × 10⁻⁴ J (D) 2 × 10⁻⁴ J (E) 2 × 10⁻⁷ 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 (A) 1/V (B) 1/√V (C) √V (D) V (E) V²

A solid metallic sphere of radius R has charge Q uniformly distributed on its outer surface. A graph of electric potential V as a function of position r is shown above. Which of the following graphs best represents the magnitude of the electric field E as a function of position r for this sphere? (A) Graph A (B) Graph B (C) Graph C (D) Graph D (E) Graph E

As shown in the figure above six particles each with charge +Q are held fixed and are 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 (B) 6Q/4πεoR² (C) 2√3Q/4πεoR² (D) 3√2Q/4πεoR² (E) 3Q/2πεoR²

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? (A) 0 (B) 6Q/4πεoR (C) 3Q²/2πεoR² (D) 3Q²/2πεoR (E) 9Q²/πεoR

The diagram above shows equipotential lines produced by an unknown charge distribution. A B C D and E are points in the plane. Which vector below best describes the direction of the electric field at point A? (A) Vector A (B) Vector B (C) Vector C (D) Vector D (E) None of these; the field is zero

At which point does the electric field have the greatest magnitude? (A) A (B) B (C) C (D) D (E) E

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? (A) -20 μJ (B) -10 μJ (C) 10 μJ (D) 20 μJ (E) 30 μJ

A physics problem starts: A solid sphere has charge distributed uniformly throughout. It may be correctly concluded that the (A) electric field is zero everywhere inside the sphere (B) electric field inside the sphere is the same as the electric field outside (C) electric potential on the surface of the sphere is not constant (D) electric potential in the center of the sphere is zero (E) sphere is not made of metal

The two plates of a parallel-plate capacitor are a distance d apart and are mounted on insulating supports. A battery is connected across the capacitor to charge it and is then disconnected. The distance between the insulated plates is then increased to 2d. If fringing of the field is still negligible which of the following quantities is doubled? (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

A parallel-plate capacitor has a capacitance Co. A second parallel-plate capacitor has plates with twice the area and twice the separation. The capacitance of the second capacitor is most nearly (A) ¼Co (B) ½Co (C) Co (D) 2Co (E) 4Co

Three 6-microfarad capacitors are connected in series with a 6-volt battery. The equivalent capacitance of the set of capacitors is (A) 0.5 μF (B) 2 μF (C) 3 μF (D) 9 μF (E) 18 μF

The energy stored in each capacitor is (A) 4 μJ (B) 6 μJ (C) 12 μJ (D) 18 μJ (E) 36 μJ

An isolated capacitor with air between its plates has a potential difference Vo and a charge Qo. After the space between the plates is filled with oil the difference in potential is V and the charge is Q. Which of the following pairs of relationships is correct? (A) Q=Qo and V>Vo (B) Q=Qo and V<Vo (C) Q>Qo and V=Vo (D) Q<Qo and V<Vo (E) Q>Qo and V>Vo

When two identical parallel-plate capacitors are connected in series which of the following is true of the equivalent capacitance? (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

Which of the following can be used along with fundamental constants but no other quantities to calculate the magnitude of the electric field between the plates of a parallel-plate 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

Two square parallel-plate capacitors of capacitances C1 and C2 have the dimensions shown in the diagrams above. The ratio of C1 to C2 is (A) 1 to 4 (B) 1 to 2 (C) 1 to 1 (D) 2 to 1 (E) 4 to 1

A sheet of mica is inserted between the plates of an isolated charged parallel-plate capacitor. Which of the following statements is true? (A) The capacitance decreases (B) The potential difference across the capacitor decreases (C) The energy of the capacitor does not change (D) The charge on the capacitor plates decreases (E) The electric field between the capacitor plates increases

The system of six 2-microfarad capacitors shown. The equivalent capacitance of the system of capacitors is (A) 2/3 μF (B) 4/3 μF (C) 3 μF (D) 6 μF (E) 12 μF

What potential difference must be applied between points X and Y so that the charge on each plate of each capacitor will have magnitude 6 microcoulombs? (A) 1.5 V (B) 3 V (C) 6 V (D) 9 V (E) 18 V

Which of the following capacitors each of which has plates of area A would store the most charge on the top plate for a given potential difference V? (A) Config A (B) Config B (C) Config C (D) Config D (E) Config E

A parallel-plate capacitor has charge +Q on one plate and charge -Q on the other. The plates each of area A are a distance d apart and are separated by a vacuum. A single proton of charge +e released from rest at the surface of the positively charged plate will arrive at the other plate with kinetic energy proportional to (A) edQ/A (B) eQ²/Ad (C) QeA/d (D) edQ (E) eQ²/Ad

Three identical capacitors each of capacitance 3.0 μF are connected in a circuit with a 12 V battery as shown above. The equivalent capacitance between points X and Z is (A) 1.0 μF (B) 2.0 μF (C) 4.5 μF (D) 6.0 μF (E) 9.0 μF

The potential difference between points Y and Z is (A) zero (B) 3 V (C) 4 V (D) 8 V (E) 9 V

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 Vo by a battery which is then disconnected. If any edge effects are negligible what is the magnitude of the electric field between the plates? (A) Vod (B) Vo/d (C) d/Vo (D) Vo/d² (E) Vo²/d

A sheet of insulating plastic material is inserted between the plates without otherwise disturbing the system. What effect does this have on the capacitance? (A) It causes the capacitance to increase (B) It causes the capacitance to decrease (C) None; the capacitance does not change (D) Nothing can be said about the effect without knowing the dielectric constant of the plastic (E) Nothing can be said about the effect without knowing the thickness of the sheet

Three 1/2 μF capacitors are connected in series as shown in the diagram above. The capacitance of the combination is (A) 0.1 μF (B) 1 μF (C) 2/3 μF (D) ½ μF (E) 1/6 μF

The plates of a parallel-plate capacitor of cross sectional area A are separated by a distance d as shown above. Between the plates is a dielectric material of constant K. The plates are connected in series with a variable resistance R and a power supply of potential difference V. The capacitance C of this capacitor will increase if which of the following is decreased? (A) A (B) R (C) K (D) d (E) V