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 = 0.14 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

emf = B*l*v

induced current = I = e/R

R = L/A.

magnetic force Fb = B*I*l = B*e*A*l/l = B*B*l*v*A*l/l (up wards)

Fb = B^2*A*l^2*v/

gravitational force Fg = m*g = d*V*g = d*A*l*g (down wards)

Fb = Fg

B^2*A*l*v/ = d*A*l*g

v = d*g*/B^2

v = (9*10^3*9.8*1.7*10^-8)/(0.14^2)

v = 0.076 m/s

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