The diagram below shows two metal rails, a distance L = 20 cm apart; the rails h

Question

The diagram below shows two metal rails, a distance L = 20 cm apart; the rails have no resistance. A metal bar of resistance R_3 = 20 ohm is being pulled across the frictionless rails at a constant speed v = 5 m/s. There are also two resistors connecting the two rails: R_1 = 10 ohm and R_2 = 14 ohm. A uniform magnetic field (not shown) points out of the page, and has magnitude B = 0.08 T. (a) Determine the current in each resistor, and in the metal bar that's being pulled. (b) Calculate the applied force on the metal bar (that's the force being exerted by whatever is pulling it to the right). (c) Calculate the power delivered by the applied force, by using the general formula for power delivered by a force. (d) Calculate the total power dissipated as heat in the resistors and the metal bar, by using the formula for power dissipated in a resistor. (e) Check whether or not your answers to (c) and (d) are the same. Should they be the same?

Explanation / Answer

a)

Induced emf

E=BLv=0.08*0.2*5

E=0.08 Volts

Current through each resistor is

I1=E/R1=0.08/10=0.008 A

I2=E/R2=0.08/14=0.0057 A

b)

total current

I=0.008+0.0057=0.0137 A

applied force on metal bar

F=BIL=0.08*0.0137*0.2

F=2.2*10-4 N

c)

Power delivered by applied force

P=Fv=2.2*10-4*5=1.1*10-3 W

d)

power dissipated in resistors

P=EI=0.08*0.0137=1.1*10-3 W

e)

yes ,they should be same

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