A force ~F is applied to a conducting rod so that the rod slides with constant s

Question

A force ~F is applied to a conducting rod so that the rod slides with constant speed 7.4 m/s over a frictionless pair of parallel conducting rails that are separated by a distance 0.75 m. The rod and rails have negligible resistance, but the rails are connected by a resistance 21 ohm. There is a uniform magnetic field 0.06 T perpendicular to and directed out of the the plane of the paper. (1) What is the direction of the induced current in the resistor R. A. Going down through the resistor B. Going up through the resistor.

(2)Determine the magnitude of the induced emf in the rod. Answer in units of V

(3)Determine the electric field in the rod. Answer in units of V/m

(4)Determine the magnitude of the induced current in the resistor R. Answer in units of A

(5)Determine the power dissipated in the resistor as the rod moves in the magnetic field. Answer in units of W

(6)Determine themagnitude of the external force applied to the rod to keep it moving with constant speed 7.4 m/s. Answer in units of N

Explanation / Answer

A force ~F is applied to a conducting rod so that the rod slides with constant speed 7.4 m/s over a frictionless pair of parallel conducting rails that are separated by a distance 0.75 m. The rod and rails have negligible resistance, but the rails are connected by a resistance 21 ohm. There is a uniform magnetic field 0.06 T perpendicular to and directed out of the the plane of the paper.

(1) What is the direction of the induced current in the resistor R.

B. Going up through the resistor.

(2)Determine the magnitude of the induced emf in the rod. Answer in units of V

emf = B L v = 0.06*0.75*7.4 = 0.333 = 0.33 V

(3)Determine the electric field in the rod. Answer in units of V/m

(4)Determine the magnitude of the induced current in the resistor R. Answer in units of A

i = V/R = 0.333/21 = 0.015857 = 0.016 A

(5)Determine the power dissipated in the resistor as the rod moves in the magnetic field. Answer in units of W

F = i L B = 0.015857*0.75*0.06 = 0.000713565 N

P = F v = 0.000713565*7.4 = 0.005280381 = 0.0053 W

(6)Determine themagnitude of the external force applied to the rod to keep it moving with constant speed 7.4 m/s. Answer in units of N

F = i L B = 0.015857*0.75*0.06 = 0.000713565 = 0.00071 N

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