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 $$30$$-$$\muF $$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 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}$$)^2$$}$

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 $$R_1$$ \u003c r \u003c $$R_2$$?

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 $$30$$-$$\muF $$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 $$C = 30 \muF. $$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 $$30$$-$$\muF $$capacitor is charged to $$10.0 V $$and then disconnected from the battery. It is then connected in parallel with an uncharged $$30$$-$$\muF$ $$ 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 $$30$$-$$\muF $$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 $$30$$-$$\muF $$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

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