Problem 23.39 The figure(Figure 1) shows a zero-resistance rod sliding to the ri

Question

Problem 23.39

The figure(Figure 1) shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.491 m . The rails are connected by a 12.9 ? resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.813 T .

Part A

Find the force that must be exerted on the rod to maintain a constant current of 0.160 A in the resistor in mN?

Part B

What is the rate of energy dissipation in the resistor in W?

Part C

What is the mechanical power delivered to the rod in W?

Explanation / Answer

Here,

L = 0.491 m

R = 12.9 Ohm

magnitude of magnetic field , B = 0.813 T

part A)

force exerted on the current = B*I*L

force exerted on the current = 0.813 * 0.160 * 0.491

force exerted on the current = 0.064 N

force exerted on the current = 64 mN

part B)

rate of energy dissipation = I^2 * R

rate of energy dissipation = 0.16^2 * 12.9

rate of energy dissipation = 0.33 W

part C)

mechanical power delivered = FOrce * velocity

mechanical power delivered = rate of energy dissipation

mechanical power delivered = 0.33 W

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