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AP Physics C: Electricity and Magnetism Unit 1: Electrostatics

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Unit 1: Electrostatics

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Question 1

An infinitely long line charge has linear charge density $λ > 0$ . Using Gauss's law with a coaxial cylindrical Gaussian surface of radius $r$ and length $L$ , the electric field at distance $r$ from the line is:

E = \frac{λ}{2 π ϵ _{0} r ^{2}}

E = \frac{λ}{2 π ϵ _{0} r}

E = \frac{λ L}{2 π ϵ _{0} r}

E = \frac{λ}{4 π ϵ _{0} r}

Question 2

Two point charges $q_{1} = + 3 μ C$ and $q_{2} = - 3 μ C$ are separated by $r = 0.30 m$ . Using $k = 9 \times 1 0^{9} N\cdotm^{2} / C^{2}$ , the magnitude of the electric force between them is:

0.90 N

0.30 N

0.10 N

8.1 \times 1 0^{- 3} N

Question 3

The electric potential in a region is $V (x, y) = 3 x^{2} y - y^{3}$ (in volts, with $x, y$ in meters). The $x$ -component of the electric field at the point $(1, 1)$ is:

E_{x} = - 6 V/m

E_{x} = + 6 V/m

E_{x} = - 3 V/m

E_{x} = + 3 V/m

Question 4

The electric potential at a distance $r$ from the center of a uniformly charged insulating sphere of radius $R$ and total charge $Q$ , for $r < R$ , is:

V (r) = \frac{k Q}{r}

V (r) = \frac{k Q}{2 R} (3 - \frac{r ^{2}}{R ^{2}})

V (r) = \frac{k Q}{R}

V (r) = \frac{k Q r ^{2}}{R ^{3}}

Question 5

A spherical conducting shell of inner radius $a$ and outer radius $b$ carries a net charge $+ Q$ . A point charge $+ q$ is placed at the center. By Gauss's law, the surface charge density on the outer surface of the shell is:

σ_{outer} = \frac{Q}{4 π b ^{2}}

σ_{outer} = \frac{Q + q}{4 π b ^{2}}

σ_{outer} = \frac{Q - q}{4 π b ^{2}}

σ_{outer} = \frac{q}{4 π b ^{2}}

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Question 6

An infinite plane of charge has surface charge density $σ$ . Using Gauss's law with a pillbox Gaussian surface that straddles the sheet, the electric field magnitude on each side of the sheet is:

E = \frac{σ}{ϵ _{0}}

E = \frac{σ}{2 ϵ _{0}}

E = \frac{2 σ}{ϵ _{0}}

E = \frac{σ}{4 π ϵ _{0}}

Question 7

Two large parallel conducting plates separated by distance $d$ each carry surface charge density $+ σ$ and $- σ$ respectively. A small conducting sphere of radius $a ≪ d$ with net charge $q$ is held midway between the plates. Ignoring image charges, the electric force on the sphere is:

F = q σ / ϵ_{0}

, directed from the positive to the negative plate.B.

F = q σ / (2 ϵ_{0})

, directed from the positive to the negative plate.C.

F = 0

, because the sphere is midway between the plates.D.

F = 2 q σ / ϵ_{0}

, directed from the positive to the negative plate.

Question 8

A solid insulating sphere of radius $R$ carries uniform volume charge density $ρ$ . For a point inside the sphere at radius $r < R$ , Gauss's law gives the electric field magnitude:

E = \frac{ρ R ^{3}}{3 ϵ _{0} r ^{2}}

E = \frac{ρ r}{3 ϵ _{0}}

E = \frac{ρR}{3 ϵ _{0}}

E = 0

Question 9

A uniformly charged thin ring of radius $R$ and total charge $Q$ lies in the $x y$ -plane centered at the origin. The electric field on the axis of the ring at distance $z$ from the center points:

A.Radially outward from the ring's center, perpendicular to the axis.B.Along the

z

-axis (axial direction) for

z \neq = 0

.C.In the plane of the ring, toward the nearest point of the ring.D.Zero everywhere on the axis.

Question 10

A finite line segment of length $2 L$ lies along the $x$ -axis, centered at the origin, with uniform linear charge density $λ$ . What is the electric potential $V$ at a point $P$ on the perpendicular bisector (the $y$ -axis) at distance $d$ from the origin?

V = \frac{λ}{2 π ϵ _{0}} ln (\frac{L + L ^{2} + d ^{2}}{d})

V = \frac{λ L}{2 π ϵ _{0} d}

V = \frac{λ}{4 π ϵ _{0}} ln (\frac{L + d}{L - d})

V = \frac{λ}{2 π ϵ _{0}} ln (\frac{d}{L + L ^{2} + d ^{2}})

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Question 11

A thin disk of radius $R$ has uniform surface charge density $σ$ . Using integration over rings, the electric field at a point on the axis of the disk at distance $z$ from the center is:

E = \frac{σ}{2 ϵ _{0}} (1 - \frac{z}{z ^{2} + R ^{2}})

E = \frac{σ}{2 ϵ _{0}} (1 + \frac{z}{z ^{2} + R ^{2}})

E = \frac{σ R}{2 ϵ _{0} z ^{2} + R ^{2}}

E = \frac{σ z}{2 ϵ _{0} ( z ^{2} + R ^{2} )}

Question 12

A solid insulating cylinder of radius $R$ and infinite length has non-uniform volume charge density $ρ (r) = ρ_{0} r / R$ , where $r$ is the distance from the axis. Using Gauss's law, the electric field magnitude for $r < R$ is:

E = \frac{ρ _{0} r ^{2}}{3 ϵ _{0} R}

E = \frac{ρ _{0} r}{3 ϵ _{0}}

E = \frac{ρ _{0} r ^{2}}{2 ϵ _{0} R}

E = \frac{ρ _{0} R}{3 ϵ _{0}}

AP Physics C: Electricity and Magnetism Unit 1: Electrostatics — Free with Answer Explanations | Test Practice Hub