A thin, 54.0 cm long metal bar with mass 710 g rests on, but is not attached to,

Question

A thin, 54.0 cm long metal bar with mass 710 g rests on, but is not attached to, two metallic supports in a uniform magnetic field with a magnitude of 0.490 T , as shown in the figure (Figure 1) . A battery and a resistor of resistance 22.0 are connected in series to the supports.

Part A

What is the largest voltage the battery can have without breaking the circuit at the supports?

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Part B

The battery voltage has the maximum value calculated in part (a). If the resistor suddenly gets partially short-circuited, decreasing its resistance to 3.00 , find the initial acceleration of the bar.

A thin, 54.0 cm long metal bar with mass 710 g rests on, but is not attached to, two metallic supports in a uniform magnetic field with a magnitude of 0.490 T , as shown in the figure (Figure 1) . A battery and a resistor of resistance 22.0 are connected in series to the supports.

Part A

What is the largest voltage the battery can have without breaking the circuit at the supports?

SubmitMy AnswersGive Up

Part B

The battery voltage has the maximum value calculated in part (a). If the resistor suddenly gets partially short-circuited, decreasing its resistance to 3.00 , find the initial acceleration of the bar.

Explanation / Answer

a)

magnetic force balances weight of bar

hence Fb = mg

i B L= mg

i (0.49) (0.54) = (0.71) (9.8)

i = 26.3 A

largest Voltage = Vmax = i R = 26.3 x 22 = 578.6 volts

b)

i' = current when short circuited = Vmax /R' = 578.6/3 = 192.87 A

net force is then given as

Fnet = i'BL - mg

ma = i'BL - mg

(0.71) a = (192.87) (0.490) (0.54) - (0.71) (9.8)

a = 62.1 m/s2

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