EXAMPLE 20.4Where Is the Energy Source? GOAL Use motional emf to find an induced

Question

EXAMPLE 20.4Where Is the Energy Source? GOAL Use motional emf to find an induced emf and a opposes the motion, and a s indeced in the loo PROBLEM (a) The sliding bar in the figure has a length of 0.500 m and moves at 2.00 m/s in a magnetic field of magnitude 0.250 T. Using the concept of motional emf, find the induced voltage in the moving rod. (b) If the resistance in the circuit is 0.500 ?, find the current in the circuit and the power delivered to the resistor. (Note: The current in this case goes counterclockwise around the loop.) (c) Calculate the magnetic force on the bar. (d) Use the concepts of work and power to calculate the applied force. STRATEGY For part (a), substitute into for the motional emf. Once the emf is found, substitution into Ohm's law gives the current. In part (c), use F-ssine for the magnetic force on a current-carrying conductor. In part (d), use the fact that the power dissipated by the resistor multiplied by the elapsed time must equal the work done by the applied force SOLUTION (a) Find the induced emf with the concept of motional emf. -B-(0.250 TXO.S500 m)(2.00 ms) -0.250 V (b) Find the induced current in the circuit and the power dissipated by the resistor. Substitute the em ?0.250v ?. 0.250 vtond the power dissipated by the 0.500-42 res stor (c) Calculate the magnitude and direction of the magnetic force on the bar Substitube values for 1, B, and E into the esuatien, wih -6.25), 10-2 N ure-san(SO*)·1, to find the magnitude of the foe

Explanation / Answer

a) Using the relation for induced voltage, V=B*L*v

V= 0.229*0.456*1.5= 0.157 V

b) Current, I = V/R = 0.157/0.3 = 0.522 A

Power delivered to the resistor, P= V*I = 0.157*0.522= 0.08 W

c) Magnetic force on the bar, F = I*B*L= 0.522*0.229*0.456= 0.05 N

According to right hand rule F is in -ve x direction.

d) Work done= power*time

Fapp = P*t/(v*t)= =P/v= 0.08/1.5= 0.05 N

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