A stiff spring with a spring constant of 2000.0 N/m is connected to a bar on a s

Question

A stiff spring with a spring constant of 2000.0 N/m is connected to a bar on a slide generator as shown in the figure below. Assume the bar has length ? = 59.0 cm and mass m = 0.75 kg, and it slides without friction. The bar connects to a U-shaped wire to form a loop that has width w = 40.0 cm and total resistance 27 ? and that sits in a uniform magnetic field B = 0.35 T. The bar is initially pulled 5.0 cm to the left and released so that it begins to oscillate. What is the induced current in the loop as a function of time, I(t)? (Ignore any effects due to the magnetic force on the oscillating bar. Assume clockwise current is positive. Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that I is in amps and t is in seconds. Do not include units in your answer.

I(t)=?

Explanation / Answer

induced emf = B.dA/dt

T = 2pi*sqrt(m/k)

T = 0.1216 sec

Change in area dA = l*(0.1) = 0.59*( w+0.05 - w-0.05)

dA = 0.59*0.1 = 0.059 m^2

e = 0.35*0.059/0.1216

e= 0.1698 V

I = e/R = 0.1698/27 = 6.28*10^-3 A

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