(Numerical values are in SI units, unless specified otherwise)
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
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
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
length of rod,
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
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
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
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
PHYS 122 A,B Spring 2011
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?
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