A thin, 47.0 c m long metal bar with mass 790 g rests on, but is not attached to

Question

A thin, 47.0 cm long metal bar with mass 790 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 21.0 are connected in series to the supports.

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

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

l =47 cm , m =790 g , B =0.5 T, R =21 ohm

Magnetic force = weight of bar

FB = IlB =Fg = mg

I = mg/lB = (0.79*9.8)/(0.47*0.5) =32.94 A

From ohms law

V = IR = 32.94*21

V = 691.74 V

(b) R1 = 3 ohms

I1 = V/R1

F = FB -Fg

ma = I1lB - mg

a = (VlB/R1*m) - g

a = (691.74*0.5)/(3*0.79) - 9.8

a =136 m/s^2

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