#1-A thin, 51.0 cm long metal bar with mass 740 g rests on, but is not attached

Question

#1-A thin, 51.0 cm long metal bar with mass 740 g rests on, but is not attached to, two metallic supports in a uniform magnetic field with a magnitude of 0.430 T, as shown in the figure. A battery and a resistor of resistance 22.0 are connected in series to the supports. What is the largest voltage the battery can have without disconnecting the circuit at the supports? If the resistor suddenly gets partially short-circuited, decreasing its resistance to 2.50 , find the initial acceleration of the bar. Assume the battery voltage has the value calculated in part a) b)

Explanation / Answer

a)

Here magnetic force is balanced by magnetic force

BIL=mg

I=mg/BL =0.74*9.8/0.43*0.51

I=33.07 A

Maximum voltage of battery

V=IR =33.07*22

V=727.5 Volts

b)

when the resistor is shorted ,the current is

Is =V/Rs

since

F=FB-Fg

ma =B(V/Rs)L-mg

0.74*a =(0.43*727.5*0.51/2.5)-0.74*9.8

a=76.44 m/s2

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