The conducting rod ab shown in the figure makes contact with metal rails ca and

Question

The conducting rod ab shown in the figure makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field 0.800 T, perpendicular to the plane of the figure.

A) Find the magnitude of the emf induced in the rod when it is moving toward the right with a speed 7.50 m/s .

B) In what direction does the current flow in the rod? (Clockwise or counterclockwise)

C) If the resistance of the circuit abdc is 1.50 ?(assumed to be constant), find the magnitude of the force required to keep the rod moving to the right with a constant speed of 7.50 m/s . You can ignore friction. (Force measured in newtons to the right)

D) Find the direction of the force required to keep the rod moving to the right with a constant speed of 7.50 m/s . (Up, down, right, or left)

E) Compare the rate at which mechanical work is done by the force (Fv) with the rate at which thermal energy is developed in the circuit (I2R). (Equal or nonequal)

Explanation / Answer

part A)

emf induced = B*v*L

emf induced = 0.50 * 0.8 * 7.5

emf induced = 3 V

the emf induced in the rod is 3 V

B)

as the flux in the loop is increasing

the induced magnetic field will be oppose the applied field

the current will be ANTICLOCKWISE

c)

as the current , I =emf/R

I = 3/1.5 = 2 A

magnitude of force needed = B*I*L

magnitude of force needed = 0.8 * 2 * 0.50

magnitude of force needed = 0.8 N

d)

as the magnetic force will oppose the motion of the rod.

the magnitude of force needed will be in the direction of motion

the direction of force will be towards right

e)

rate of mechanical work done= force * velocity

rate of mechanical work done= 0.8 * 7.5

rate of mechanical work done= 6 W

the rate of mechanical work done is 6 W

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