(Numerical values are in SI units, unless specified otherwise)

05/26/2011

Force on charge in electric field F = q E

Faraday’s Law EMF = - Rate of change of Magnetic Flux

Magnetic force on current carrying wire F = I L X B

Magnetic force on a moving charge q

F= qvXB

VHall = vdrift B w w is width of conductor

Magnetic field inside a long solenoid B = μ0 n I μ0 = 4π X 10-7

Magnetic field due to a long straight current carrying wire B = ( μ0 / 2π) ( I/R)

Energy stored in an Inductor U = L I2/2 , current I(t) t is time , L is inductance

Maximum EMF from a generator = ω N A B

Velocity selector with perpendicular fields E, B selects a velocity v = E/B

Biot-Savart Law dB = ( μ0 /4π )( I dl X r / r3 )

Magnetic field at center of loop of radius R carrying current I is B = μ0 I/2R

1 Gauss = 10-4 Tesla

Force per length between two long straight wires F/L = (μ0/2π) ( I1 I2/ d )

For a charging RL circuit I(t) = Imax ( 1 - e-t/τ ), current through the circuit. I(0) = 0 .

Work = q V , 1 eV = 1.6 X 10-19

Power = V I (Watts) pico = 10-12 , nano = 10-9

τ = L/R time constant, I(t) is the

Joules

Electric charge on the proton + 1.6 X 10-19 C Mass of the proton 1.67 X 10-27 kg

Mass of the electron 9.11 X 10-31 kg

Cyclotron orbit radius

Cyclotron orbit period

R = p/qB

T = 2πR/v

where p = mv, q is charge, B is magnetic field

Induced EMF across rod moving perpendicular to a magnetic field B

EMF

= BLv

L

length of rod,

v speed

Hall Voltage VH = vd B w, vd is drift vel, B is magnetic field, w is width of conductor.

Current I = q n vd A, q is carrier charge, n is carrier density, A is conductor cross-section

PHYS 122 A,B Spring 2011

MIDTERM 3

May 26th

2011

PART I

NAME_____________________________

Last

First

Student #____________________________

Multiple Choice – Each question is worth 5 points – total 60 points

1. An electron moves with a speed of 106 m/s in a straight line in a region of perpendicularly oriented electric and magnetic fields. If the electric field (magnitude 10.0

N/C) is suddenly turned off, what is the frequency of the subsequent cyclotron motion?

(a) 2.8 x 105

(b) 8.0 x 105

(c) 11 x 105

(d) 15 x 105

(e) 23 x 105

revolutions/second

Solution: (a)

2. The two stable isotopes of Chlorine, 35Cl and 37Cl, are to be separated in a mass spectrometer. Chlorine gas composed of singly-ionized ions (charge = +e) is accelerated from rest through a potential difference V. The ions then enter a region in which there is a uniform magnetic field of 0.1 Tesla perpendicular to their motion and no electric field.

The particles are detected after they complete a semi-circular path. What is the minimum value of V for which the separation between the two isotopes is 2.0 cm at the detection region? (The mass of 35Cl is approximately equal to that of 35 protons).

(a) 0.5 kiloVolts

(b) 1.0

(c) 1.3

(d) 1.9

(e) 2.5

Solution: (d)

3. A square cross-section wire of side 1mm carries a current of 1.6 A. If the measured

Hall voltage is 1.0 μV for 1.0 Tesla perpendicular magnetic field, what is the density of the charge carriers (electrons)?

(a) 1.4 x 1027

(b) 1.0 x1028

(c) 1.4 x 1028

(d) 2.0 x1028

(e) 1.0 x 1029

per cubic meter

Solution: (b)

PHYS 122 A,B Spring 2011

MIDTERM 3

May 26th

2011

NAME:__________________________

Last

First

Student #_________________________

4. A solenoid of length 10.0 cm has 1000 turns. A particle of mass 1.00 nano-gram and charge 1.00 μC is located inside and near the center of the solenoid. If this particle exhibits cyclotron motion with time period 1.00 ms, what is the current in the solenoid?

(a) 0.08

(b) 0.50

(c) 3.14

(d) 5.00

(e) 19.7

Amps

Solution: (b)

5. Three infinitely long parallel wires are equidistant from one another and carry equal currents of 1.0 A each. If the force per unit length on one of the wires is 5