A perfectly conducting bar of length 0.60 m can slide along two perfectly conduc

Question

A perfectly conducting bar of length 0.60 m can slide along two perfectly conducting wires, as shown below. The two wires attach to the two sides of a light bulb with a resistance of 1.5 ohm. The magnetic field has magnitude 5.0 Tesla. (a) If Quincy pushes the bar to the right, will current go upward or downward through the bulb? (b) With what speed must Quincy slide the bar if he wants the bulb to release energy at a rate of 2.0 Joules per second? (c) With what force must Quincy push the bar to maintain the speed found in part b, assuming that the bar slides without friction?

Explanation / Answer

Here,

a)

L = 0.60 m

R = 1.5 Ohm

B = 5 T

if the bar is pushed to the right , as the magnetic flux in the loop is increasing the magnetic field inside the loop , due to current in the loop will be out of the page , hence , the current in the wire will be upwards

b)

let the speed of the wire is v

Now, as E = V^2/R

2 = (B * v * L)^2/R

2 =(5 * 0.60 * v)^2/1.50

v = 0.577 m/s

the speed of rod needed is 0.577 m/s

c)
force needed = B*I*L

force needed = B * (B * v*L/R) * L

force needed = 5 * (5 * 0.577 * 0.60/1.50) * 0.60

force needed = 3.46 N

the force needed is 3.46 N

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