A thin, 52.0 cm long metal bar with mass 740 g rests on, but is not attached to,

Question

A thin, 52.0 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 0.500 T , as shown in the figure (Figure 1) . A battery and a resistor of resistance 28.0 ? are connected in series to the supports.

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

b-The battery voltage has the maximum value calculated in part (a). If the resistor suddenly gets partially short-circuited, decreasing its resistance to 2.00 ? , find the initial acceleration of the bar.

Explanation / Answer

given 52.0 cm = L length of metal bar then L = 0.52 m

mass 740 g = m = 0.74kg , magnetic field with a magnitude of 0.500 T = B

and resistance 28.0 = R

a )

FB = i L B

Fg = mg

FB = Fg

i = mg / LB

i = 0.74 X 9.8 / 0.5 X 0.5

i = 7.252 / 0.25

i = 29 A

V = i R

V = 29 X 28

V = 812.224 volts

b)

ia = V / Ra

total force F = FB - Fg = ia L B - mg

= V / Ra L B - mg = ma

a = [( V / m Ra) L B] - g

a = [812.224 X 0.5 X 0.5 / 0.74 X 2] - 9.8

a = [203.056 / 1.48] - 9.8

a = 137.2 - 9.8

a = 127.4 m/s2

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