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(45 points) The rod shown below moves to the right on cssentially zcro-rcsistanc

ID: 1731712 • Letter: #

Question

(45 points) The rod shown below moves to the right on cssentially zcro-rcsistancc rails at a speed from thc resistor 5.0 ? V 4.0 cm (a) (8 points) What is the current magnetic flux through the circuit? (b) (12 points) What is the current through the 5.02 resistor? (c) (10 points) If the rod has a self-inductance of L -2.0 mH and it took 3.0 ms to get the rod up to speed v, what is the induced emf the moment the rod started to move? (d) (10 points) If the rod was in fact a solenoid with a radius of 15.0cm, how many turns of the wire would be needed to have such a self-inductance? (e) (5 points) Does the current circulate clockwise or counter-clockwise?

Explanation / Answer

Given,

v = 1.85 m/s ; B = 0.75 T ; x = 9 cm ; R = 5 Ohm

a)We know that

phi = BA

phi = 0.75 x 0.04 x 0.09 = 0.0027 Wb

Hence, phi = 0.0027 Wb = 2.7 milli Wb

b)We know that, the induced emf is

e = B l v

e = 0.75 x 0.04 x 1.85 = 0.056 V

from Ohm's law. e = IR => I = e/R

I = 0.056/5 = 0.0112 A

Hence, I = 0.0112 A = 11.2 milli Ampere

c)We know that

emf = L (di/dt)

emf = 2 x 10^-3 x (0.0112/3 x 10^-3) = 0.0075 V

Hence, emf = 0.0075 V = 7.5 milli V

d)We know that,

emf = N d(phi)/dt

emf = N B A/dt ; let t = 1 s

N = 0.056 x 1/0.75 x 0.04 x 0.09 = 20.74 turns

Hence, N = 20.74 turns = 21 turns