Q: A ray of light passes from air ($$n_a = 1.00) $$into glass ($$n_b = 1.50) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction in the glass?

$$\theta_b = \arcsin\left(\frac{n_a}{n_b} \sin \theta_a\right)$$

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

$$\sin \theta_{crit} = \frac{n_{air}}{n_{water}}$$

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 a uniform electric field $$E$$ and a uniform 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 wire is perpendicular to the field. What is the magnitude of the force on the wire?

Accepted Answer

$$F = IlB$$

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

$$\frac{F}{l} = \frac{\mu_0$ I I'}{2\pi r}$$

Question 5

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

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 side in the field 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

The energy stored in an inductor of inductance $$L$$ carrying current $$I is$$:

Accepted Answer

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

Question 11

What is the speed of electromagnetic waves in vacuum?

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 amplitude of the magnetic field $$B$$?

Accepted Answer

$$B = E / c$$

Question 13

A light wave in air has wavelength $$\lambda$$ and frequency $$f. $$What is the relationship between $$\lambda$$, $$f$$, and the speed of light $$c$$?

Accepted Answer

$$c = \lambda f$$

Question 14

A ray of light passes from air ($$n_a = 1.00) $$into glass ($$n_b = 1.50) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction in the glass?

Accepted Answer

$$	heta_b = \arcsin\left(\frac{n_a}{n_b} \sin 	heta_aight)$$

Question 15

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

Accepted Answer

$$\sin 	heta_{crit} = \frac{n_{air}}{n_{water}}$$

Question 16

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 17

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 18

A mass spectrometer uses a velocity selector and a uniform magnetic field to separate ions. If an ion of mass $$m$$ and charge $$q$$ enters the magnetic field with velocity $$v$$, what is the radius of its circular path?

Accepted Answer

$$R = \frac{m v}{|q| B}$$

Question 19

The energy density of the magnetic field in a region is given by:

Accepted Answer

$$u = \frac{B^2$}{2 \mu_0$}$$

PHY2054 Study Guide: Magnetic Fields, Electromagnetic Induction, and Electromagnetic Waves

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