A thin, 45.0 cm long metal bar with mass 730 g rests on, but is not attached to,

Question

A thin, 45.0 cm long metal bar with mass 730 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. A battery and a resistor of resistance 22.0 Ohm 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? Part B The battery voltage has the maximum value calculated in part (a). If the resistor gets partially short-circuited, decreasing resistance to 2.70 Ohm, find the initial acceleration of the bar.

Explanation / Answer

FB = I L B = Fg = m g

I = m g / l B = (0.730 * 9.8) / (0.45 * 0.490) = 32.44 A

This maximum current would occur when the voltage V from the battery balanced an IR drop across the resistor

V = I R = 32.44 * 22 = 713.68 V

b) The current jumps to I' = V / R'

F = FB - Fg = I' l b - m g = V l B / R' - m g = m a

a = V l B / R' m - g

= [(713.68 * 0.450 * 0.490) / (2.7 * 0.730)] - 9.8

a = 70.0 m/s2

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