Physics 4, Section 2         Exam 2                               April 5, 2002

Š BAdL = μ_oI     Φ_B= IBAdA Wb     F_B = qv x B = IL x B      Emf = - dΦ_B/dt 
Emf = vBL    ε_o = 8.85 x 10^-12      μ_o = 4π x 10^-7     c² = 1/(ε_o μ_o)     u_E = ε_oE²/2  J/m³
u_B = B²/(2μ_o)    |e^-| = 1.6 x 10^-19 C     V = -L di/dt     L = NΦ_B/i     
S = (E x B)/μ_o W/m²     E = cB     E = pc     E = mc²     dp/dV = (1/Ac)dp/dt 
F = ma = dp/dt     n₁ sin θ₁ = n₂ sin θ₂    sin θ_c = n₂/n₁    1/s + 1/s' = 1/f 
1/f = (n-1)(1/R₁ - 1/R₂)     f = R/2     m = -s'/s
B = (μ_o/4π)(qv x r)/r³     B = μ_oI/(2π r)     V = IR     P = F Av     P = I²R     F = qE
k = 2π/λ     ω = 2πf     f = 1/T     B = μ_oni    (inside solenoid)         1 T = 10⁴ gauss
I(t)= I_f(1 - exp(-t/[L/R]))                   I(t) = I₀exp(-t/[L/R])

1. A beam of protons moves at 3 × 10⁵ m/s through a uniform magnetic field with
    magnitude 2.0 T that is directed along the positive z-axis. The velocity of each
    proton lies in the x-z plane at an angle of 30^o to the +z-axis. Find the
    magnitude of the force on a proton.
    A) 1.2         B) 2.4         C) 3.6         D) 4.8         E) 6.2                    × 10^-14 N

2. When setting up a velocity selector for a charged particle beam using E and B
     fields, the fields should be oriented
    A) parallel to each other     B) perpendicular to each other     C) doesn't matter

3. In a velocity selector setup, if the sign of the charge of the particles in the
    beam is reversed, the direction should be reversed for
    A) one of the fields             B) neither of the fields
    C) won't work for particles of other sign

4. Which current distribution generates a B-field that falls off as 1/r ?
    A) straight line of current     B) moving point charge         C) wide current sheet

5. A long conducting wire of radius R = 4.0 cm has a uniform current I of 10.0 A.
    What is the magnetic field at r = 2.0 cm from the center of the wire?
    A) 0.01     B) 0.05         C) 0.1         D) 0.25         E) 0.5                     gauss

6. Maxwell's displacement current depends on
    A) E         B) B             C) Φ_E             D) dΦ_B/dt             E) dΦ_E/dt

7. If the N-pole of a bar magnet is pulled up away from the center of a wire loop
    on the floor, the direction of the induced current in the loop (as seen from
    above looking down) will be
    A) clockwise             B) counterclockwise

8. A coil 4.0 cm in radius, containing 500 turns, is placed in a uniform magnetic
    field that varies with time according to B = 0.012 t + 3.0 × 10^-5 t⁴. The coil is
    connected to a 600 Ω resistor, and its plane is perpendicular to the magnetic
    field. What is the current in the resistor at t = 5.0 s ?
    A) 0.11             B) 0.22         C) 0.33              D) 0.44         E) 0.55         mA

9. A sensitive electronic device of resistance 175 Ω is to be connected to a source
    of emf by a switch. The device is designed to operate with a current of 36 mA,
    but to avoid damage to the device, the current can rise to no more than 4.9 mA
    in the first 58 μs after the switch is closed. What inductance is required?
    A) 13     B) 24         C) 39         D) 48         E) 69                              mH

10. An inductor with internal resistance is connected to an ideal battery with an
     emf of 12.0 V. The current is 4.86 mA at 0.725 ms after the connection is
     completed. After a long time the current is 6.45 mA. What is the inductance of
     the inductor?
     A) 0.36         B) 0.52          C) 0.96         D) 1.24         E) 1.67                 

11. Whose law of electricity and magnetism was corrected by Maxwell?
     A) Coulomb         B) Faraday          C) Ampere        D) Lenz

12. A U-shaped wire is held in a uniform B-field perpendicular to the plane of the
     loop. A resistor is placed in series with the closed end of the wire. If a metal
     rod is placed across the two sides of the U-shape parallel to the closed end of
     the loop and moved back and forth along the wires always parallel to its
     original direction, the device will operate as a
     A) DC motor         B) DC generator         C) AC motor         D) AC generator

13. When light traveling at an angle crosses an interface between two media, the
     side with the smaller index will have the smaller angle.
     A) true             B) false

14. A ray of light is incident in air on a transparent cube whose index is 1.38. The
     light enters the top of the cube, travels through the cube, and hits the far side
     wall. What is the largest angle of incidence at the top that will produce TIR on
     the far side wall?
     A) 36.3         B) 45.0         C) 58.3         D) 72.1         E) 83.3             degrees

15. The critical angle for TIR at a liquid-air interface is 42.5^o. If a ray of light
     traveling in the liquid has an angle of incidence at the interface of 35.0^o, what
     angle does the refracted ray in the air make with the normal?
     A) 23.2             B) 34.5             C) 58.1         D) 66.4         E) 75.1     degrees

16. A ray of light is incident at 62^o on an interface between two glasses of indices
     1.70 and 1.58. If the ray originates in the slower medium, what is the angle of
     refraction?
     A) 23.2         B) 44.3             C) 51.7             D) 60.2         E) 71.8     degrees

Answers: 1-d, 2-b, 3-b, 4-a, 5-d, 6-e, 7-a, 8-a, 9-e, 10-c, 11-c, 12-d, 13-b, 14-d, 15-c, 16-e

Last modified on April 07, 2002