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

Let I is the current through loop,

when magnetic force is equal to gravitational force the loop falls with constant speed.

B*I*L = m*g

I = m*g/(B*L) --(1)

we know, induced emf = B*v*L

induced current, I = induced emf/R

= B*v*L/R   --(2)

from equations 1 and 2

B*v*L/R = m*g/(B*L)

v = m*g*R/(B^2*L^2)

multiply and devide with area A

v = m*g*R*A/(B^2*L^2*A)

= m/(L*A) * (R*A/L) *(1/B^2)

= 4*m/(4*L*A) * (R*A/L) *(1/B^2)

= 4*density*resistivity/B^2

= 4*9*10^3*1.7*10^-8/(0.14^2)

= 0.031 m/s

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