A metal bar moves along two parallel metal rails, and is connected to a light bu

Question

A metal bar moves along two parallel metal rails, and is connected to a light bulb as shown in the Figure. The whole system is immersed in a magnetic field of magnitude 0.600 T pointing out of the page. The distance between the horizontal rails is L = 1.20 m. The resistance of the light bulb is 46.0 Ohm. The bar is moved to the left by a constant force of magnitude 0.400 N Calculate the speed v of the bar when maximum power is being delivered to the light bulb. Find the magnitude and direction of the current in the bar? What is the maximum power delivered to the light bulb? What is the maximum mechanical power delivered to the bar by the force F? As the power is delivered to the light bulb what happens to the resistance of the bulb? Will this affect the speed of the rod? If yes, will it increase or decrease Will it affect the current in the light bulb? If yes, will it increase or decrease? Will the power found in part (d change? If so, will it be larger or smaller?

Explanation / Answer

B = magnetic field = 0.600 T

L = 1.20 m

R = resistance = 46 ohm

F = force = 0.400 N

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a) v= speed = ?

emf , e = BLv ( e = I*R) ( I = current)

I = B*L*v / R -----------------1

force , F = I*L*B

0.400 = I*1.20*0.600

I = 0.55 A

by putting the value of I in eq 1:

I = B*L*v / R   

0.55 = 0.600 *1.20 * v / 46

v= 35.13 m/s

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b) I = 0.55 A( as calculated above) and in clockwise direction.

c) max power , P = I2 R = ( 0.55)2*46 = 13.91 = 14 watt

d) max power by force , P = F*v = 0.400*35.13 = 14 watt

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