Q: A nonconducting spherical shell of inner radius $R_1$ and outer radius $R_2$ contains a uniform volume charge density $\rho$ throughout the shell. Using Gauss's law, what is the electric field at a distance $r$ from the center, where $R_1 < r < R_2$?

$E = \dfrac{\rho (r^3 - R_1^3)}{3 \varepsilon_0 r^2}$

Q: Two 5.0-g spheres are suspended from a common point by 1.0-m-long threads. Each sphere carries a charge of $8.0 \times 10^{-8}$ C and hangs at rest, making an angle $\theta$ with the vertical. Which equation correctly relates $\theta$ to the forces acting on the spheres?

$\tan \theta = \dfrac{F_e}{mg}$

Q: An uncharged $30$-$\mu$F capacitor is connected in series with a $25$-$\Omega$ resistor, a DC battery, and an open switch. The battery has an emf of $10.0$ V. What is the maximum charge that the capacitor receives?

$Q_{max} = C V = 30 \times 10^{-6} \times 10.0$

Q: A $20,000$-loop coil of cross-sectional area $8.5$ cm$^2$ lies in the plane of the page. An external magnetic field of $0.025$ T is perpendicular to the plane. What is the magnitude of the change in the external magnetic flux induced by the coil?

$\Delta \Phi = N \Delta B A = 20,000 \times 0.025 \times 8.5 \times 10^{-4}$

Q: A $60$-Hz AC source of the series circuit shown in the figure has a voltage amplitude of $120$ V. The capacitive reactance is $790 \Omega$, the inductive reactance is $270 \Omega$, and the resistance is $500 \Omega$. What is the impedance $Z$ of the circuit?

$Z = \sqrt{R^2 + (X_L - X_C)^2}$

Q: A laser beam has a wavelength of $633$ nm and a power of $0.500$ mW spread uniformly over a circle $1.20$ mm in diameter. What is the intensity of the beam?

$I = \dfrac{P}{A} = \dfrac{0.500 \times 10^{-3}}{\pi (0.60 \times 10^{-3})^2}$

Q: A coil with $N$ turns and area $A$ is rotated in a uniform magnetic field $B$ at angular speed $\omega$. What is the maximum emf induced in the coil?

$\varepsilon_{max} = N B A \omega$

Q: A $10$-$\Omega$ resistor and a $20$-$\Omega$ resistor are connected in parallel across a $12$-V battery. What is the total current supplied by the battery?

$I_{total} = \dfrac{V}{R_{eq}} = \dfrac{12}{\dfrac{1}{10} + \dfrac{1}{20}}^{-1}$

Q: A $5$-mH inductor and a $30$-$\mu$F capacitor are connected in series to a $120$-V, $60$-Hz AC source. What is the resonant frequency of the circuit?

$f_0 = \dfrac{1}{2 \pi \sqrt{LC}}$

Q: A $10$-$\Omega$ resistor is connected in series with a $20$-$\Omega$ resistor and a $30$-$\mu$F capacitor to a $120$-V, $60$-Hz AC source. What is the average power dissipated by the circuit?

$P_{avg} = V_{rms} I_{rms} \cos \phi$

Question 1

A nonconducting spherical shell of inner radius $R_1$ and outer radius $R_2$ contains a uniform volume charge density $\rho$ throughout the shell. Using Gauss's law, what is the electric field at a distance $r$ from the center, where $R_1 < r < R_2$?

Accepted Answer

$E = \dfrac{\rho (r^3 - R_1^3)}{3 \varepsilon_0 r^2}$

Question 2

Two 5.0-g spheres are suspended from a common point by 1.0-m-long threads. Each sphere carries a charge of $8.0 	imes 10^{-8}$ C and hangs at rest, making an angle $	heta$ with the vertical. Which equation correctly relates $	heta$ to the forces acting on the spheres?

Accepted Answer

$	an 	heta = \dfrac{F_e}{mg}$

Question 3

A pair of charged conducting plates produces a uniform field of $12,000$ N/C, directed to the right, between the plates. The separation of the plates is $40$ mm. An electron is projected from plate A, directly toward plate B, with an initial velocity of $1.60 	imes 10^6$ m/s. What is the distance of closest approach of the electron to plate B?

Accepted Answer

$d = \dfrac{m v^2}{2 e E}$

Question 4

Consider the circuit shown with two batteries and three resistors. If $R_1 = 4.0 \Omega$, $R_2 = 6.0 \Omega$, $R_3 = 8.0 \Omega$, and the batteries are $6.0$ V and $3.0$ V, what is the current $I_1$ through $R_1$?

Accepted Answer

$I_1 = \dfrac{6.0}{4.0}$

Question 5

An uncharged $30$-$\mu$F capacitor is connected in series with a $25$-$\Omega$ resistor, a DC battery, and an open switch. The battery has an emf of $10.0$ V. What is the maximum charge that the capacitor receives?

Accepted Answer

$Q_{max} = C V = 30 	imes 10^{-6} 	imes 10.0$

Question 6

A $20,000$-loop coil of cross-sectional area $8.5$ cm$^2$ lies in the plane of the page. An external magnetic field of $0.025$ T is perpendicular to the plane. What is the magnitude of the change in the external magnetic flux induced by the coil?

Accepted Answer

$\Delta \Phi = N \Delta B A = 20,000 	imes 0.025 	imes 8.5 	imes 10^{-4}$

Question 7

A $60$-Hz AC source of the series circuit shown in the figure has a voltage amplitude of $120$ V. The capacitive reactance is $790 \Omega$, the inductive reactance is $270 \Omega$, and the resistance is $500 \Omega$. What is the impedance $Z$ of the circuit?

Accepted Answer

$Z = \sqrt{R^2 + (X_L - X_C)^2}$

Question 8

An LRC series circuit has $R = 15 \Omega$, $L = 25$ mH, and $C = 30 \mu$F. The circuit is connected to a $120$-V source with frequency $200$ Hz. What is the power factor (cos$\phi$) for the circuit?

Accepted Answer

$\cos \phi = \dfrac{R}{Z}$

Question 9

A sinusoidal electromagnetic wave is propagating in vacuum. At a given point $P$ and at a particular time, the electric field is in the $y$-direction and the magnetic field is in the $z$-direction. What is the direction of propagation of the wave?

Accepted Answer

In the $x$-direction

Question 10

A laser beam has a wavelength of $633$ nm and a power of $0.500$ mW spread uniformly over a circle $1.20$ mm in diameter. What is the intensity of the beam?

Accepted Answer

$I = \dfrac{P}{A} = \dfrac{0.500 	imes 10^{-3}}{\pi (0.60 	imes 10^{-3})^2}$

Question 11

A $30$-$\mu$F capacitor is charged to $10.0$ V and then disconnected from the battery. It is then connected in parallel with an uncharged $30$-$\mu$F$ $ capacitor. What is the final voltage across both capacitors?

Accepted Answer

$V_f = \dfrac{V_0}{2}$

Question 12

A coil with $N$ turns and area $A$ is rotated in a uniform magnetic field $B$ at angular speed $\omega$. What is the maximum emf induced in the coil?

Accepted Answer

$\varepsilon_{max} = N B A \omega$

Question 13

A $10$-$\Omega$ resistor and a $20$-$\Omega$ resistor are connected in parallel across a $12$-V battery. What is the total current supplied by the battery?

Accepted Answer

$I_{total} = \dfrac{V}{R_{eq}} = \dfrac{12}{\dfrac{1}{10} + \dfrac{1}{20}}^{-1}$

Question 14

A $5$-mH inductor and a $30$-$\mu$F capacitor are connected in series to a $120$-V, $60$-Hz AC source. What is the resonant frequency of the circuit?

Accepted Answer

$f_0 = \dfrac{1}{2 \pi \sqrt{LC}}$

Question 15

A $10$-$\Omega$ resistor is connected in series with a $20$-$\Omega$ resistor and a $30$-$\mu$F capacitor to a $120$-V, $60$-Hz AC source. What is the average power dissipated by the circuit?

Accepted Answer

$P_{avg} = V_{rms} I_{rms} \cos \phi$

Question 16

A sinusoidal electromagnetic wave in vacuum has an electric field amplitude $E_0$ and a magnetic field amplitude $B_0$. What is the relationship between $E_0$ and $B_0$?

Accepted Answer

$E_0 = c B_0$

Question 17

A $0.500$-mW laser beam of wavelength $633$ nm is incident on a perfectly reflecting piece of paper having a mass of $1.50$ g. What is the acceleration given to the paper by the laser beam?

Accepted Answer

$a = \dfrac{2 P}{c m}$

Practice Final Exam Study Guide: Electricity, Magnetism, and Electromagnetic Waves

Study Guide - Practice Questions

Study Guide - Flashcards