A square loop made of copper wire is falling out of a region where there is a ma

Question

A square loop made of copper wire is falling out of a region where there is a magnetice field Bext = 0.13 T. The loop is falling with a constant velocity because of the current induced in the loop. What is the velocity of the loop? Give your answer in m/s to at least three significant digits. It will be useful to know that: The mass density of copper (mass per volume) is 9.0x103 kg/m3. The resistivity of copper is ? = 1.7x10-8 ?-m. Remember that the resistance of a wire of length L and cross-sectional area A is R = ? L/A.

Explanation / Answer

induced emf in the loop is given as

E = BLV

R = resistance of wire

so current in the loop is given as

i = E/R = BLV/R

magnetic force acting on the side of loop = F = iBL = (BLV/R)BL = B2L2V/R

the magnetic force balances the weight of the loop , hence

F = mg

B2L2V/R = mg

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