A conducting rod of length L = 10.0 cm and mass m = 5.00 g is resting on two ele

Question

A conducting rod of length L = 10.0 cm and mass m = 5.00 g is resting on two electrical contacts which connect it to the rest of the electrical circuit as shown. Take the rod's resistance and resistance of these two contacts to be zero. The rod is in the uniform magnetic field B = 0.35 T pointing into the page. The battery has emf epsilon = 30.0 V and internal resistance r = 2.50 ohm. The switch is initially open. At what range of values of R will the rod float in space (will not press on the two contacts) upon closing of the switch?

Explanation / Answer

I = (30 - I r) / R the current thru thecircuit I = 30 / (R + r) F = I L B       the force on acurrent-carrying wire due to magnetic field B m g = 30 L B / (R + r) R = (30 L B - m g r) / (m g) R = (30 * .1 * .35 - .005 * 9.8 * 2.5) / .005 * 9.8) = 18.9 So R must be less than 18.9

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