Q: A light wave in air ($$n=1) $$enters glass ($$n=1.5) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction in the glass?

$$\theta_b = \arcsin\left(\frac{n_a}{n_b} \sin \theta_a\right) = \arcsin\left(\frac{1}{1.5} \sin 30^\circ\right) \approx 19.5^\circ$$

Q: What is the critical angle for total internal reflection for light traveling from water ($$n=1.33) to $$air ($$n=1.00$$)?

$$\theta_{crit} = \arcsin\left(\frac{n_b}{n_a}\right) = \arcsin\left(\frac{1.00}{1.33}\right) \approx 48.8^\circ$$

Q: A mass spectrometer uses a velocity selector with $$E = 2.0 \times 10^4$\ \mathrm{V/m}$$ and $$B = 0.50\ \mathrm{T}. $$What velocity will pass through undeflected?

$$v = \frac{E}{B} = \frac{2.0 \times 10^4$}{0.50} = 4.0 \times 10^4$\ \mathrm{m/s}$$

Q: A long straight wire carries a current of $$5\ \mathrm{A}. $$What is the magnetic field $$0.10\ \mathrm{m}$$ from the wire?

$$B = \frac{\mu_0$ I}{2\pi r} = \frac{4\pi \times 10$$^{-7}$$ \times 5}{2\pi \times 0.10} = 1.0 \times 10$$^{-5}$$\ \mathrm{T}$$

Question 1

A proton moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the magnitude of the force acting on the proton?

Accepted Answer

$$F = qvB$$

Question 2

A charged particle enters a region with both electric field $$E$$ and magnetic field $$B$$ perpendicular to each other. If the particle passes through undeflected, what is its velocity?

Accepted Answer

$$v = E/B$$

Question 3

A wire of length $$l$$ carries a current $$I$$ and is placed in a uniform magnetic field $$B$$ such that the angle between the wire and the field is $$\phi. $$What is the magnitude of the force on the wire?

Accepted Answer

$$F = IlB \sin \phi$$

Question 4

Two long, parallel conductors carry currents $$I$$ and $$I' in $$the same direction and are separated by a distance $$r. $$What is the force per unit length between them?

Accepted Answer

$$\frac{\mu_0$ I I'}{2\pi r}$$

Question 5

What is the magnetic field at the center of a circular loop of radius $$R$$ carrying current $$I$$ with $$N$$ turns?

Accepted Answer

$$B = \frac{\mu_0$ N I}{2R}$$

Question 6

A solenoid has $$n$$ turns per unit length and carries a current $$I. $$What is the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I$$

Question 7

According to Faraday's law, what is the induced emf in a coil of $$N$$ turns if the magnetic flux changes by $$\Delta \Phi_B in $$time $$\Delta t$$?

Accepted Answer

$$\epsilon = N \frac{\Delta \Phi_B}{\Delta t}$$

Question 8

A rectangular loop of wire moves at constant velocity $$v$$ perpendicular to a uniform magnetic field $$B. If $$the length of the loop in the direction of motion is $$L$$, what is the induced emf?

Accepted Answer

$$\epsilon = B L v$$

Question 9

A transformer has a primary coil with $$N_1$$ turns and a secondary coil with $$N_2$$ turns. If the input voltage is $$V_1$$, what is the output voltage $$V_2$$?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$N_2$$}{$$N_1$$}$$

Question 10

What is the energy stored in an inductor of inductance $$L$$ carrying current $$I$$?

Accepted Answer

$$U = \frac{1}{2} L I^2$

Question 11

What is the speed of light in vacuum in terms of the permittivity $$\$$epsilon_0$$ and permeability $$\$$mu_0 of $$free space?

Accepted Answer

$$c = \frac{1}{\sqrt{\$$epsilon_0$$ \mu_0$}}$$

Question 12

If the electric field amplitude of an electromagnetic wave is $$E$$, what is the corresponding magnetic field amplitude $$B$$?

Accepted Answer

$$B = E / c$$

Question 13

A light wave in air ($$n=1) $$enters glass ($$n=1.5) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction in the glass?

Accepted Answer

$$	heta_b = \arcsin\left(\frac{n_a}{n_b} \sin 	heta_aight) = \arcsin\left(\frac{1}{1.5} \sin 30^\circight) \approx 19.5^\circ$$

Question 14

What is the critical angle for total internal reflection for light traveling from water ($$n=1.33) to $$air ($$n=1.00$$)?

Accepted Answer

$$	heta_{crit} = \arcsin\left(\frac{n_b}{n_a}ight) = \arcsin\left(\frac{1.00}{1.33}ight) \approx 48.8^\circ$$

Question 15

Unpolarized light of intensity $$I_0$$ passes through a polarizer. What is the intensity of the transmitted light?

Accepted Answer

$$I_1$$ = $$I_0 / 2$

Question 16

Linearly polarized light of intensity $$I_{max}$$ passes through a polarizing filter with its axis at an angle $$\phi to $$the direction of polarization. What is the transmitted intensity?

Accepted Answer

$$I = I_{max} \cos^2$ \phi$$

Question 17

A mass spectrometer uses a velocity selector with $$E = 2.0 	imes 10^4$\ \mathrm{V/m}$$ and $$B = 0.50\ \mathrm{T}. $$What velocity will pass through undeflected?

Accepted Answer

$$v = \frac{E}{B} = \frac{2.0 	imes 10^4$}{0.50} = 4.0 	imes 10^4$\ \mathrm{m/s}$$

Question 18

A long straight wire carries a current of $$5\ \mathrm{A}. $$What is the magnetic field $$0.10\ \mathrm{m}$$ from the wire?

Accepted Answer

$$B = \frac{\mu_0$ I}{2\pi r} = \frac{4\pi 	imes 10$$^{-7}$$ 	imes 5}{2\pi 	imes 0.10} = 1.0 	imes 10$$^{-5}$$\ \mathrm{T}$$

PHY2054 Exam Review: Magnetic Fields, Electromagnetic Induction, and Electromagnetic Waves

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