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 = 0.04 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

Here ,

let the constant speed is v m/s

let the length of side is l

A is the cross section the wire used ,

d is the density of copper

as the current induced in the loop ,

I = B*v*l/R

NOw , for the loop to fall with constant velocity

B*I*L = m * g

B*l * B*v*l/R = 4 * l * A * d * g

B^2 * l^2 * v /(p * 4 l/A) = 4 * l * A * d * g

B^2 * l * A * v/(4 * p) = 4 * l * A * d * g

B^2 * v/(4 * p) = 4 * d * g

0.04^2 * v /(4 * 1.7 *10^-8) = 4 * 9000 * 9.8

solving for v

v = 15 m/s

the constant speed of the loop is 15 m/s

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