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 = 0.09 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

for constant speed of the loop

magnetic force F = mg = iLB

here i = mg/LB

since density D = mass/Volume = m/V -----< m = DV = D * AL

i = (D * AL) * g /LB

where m is mass and g is accleration due to gravity

i is current L is length and B is magnetic field

also induced emf e = V = lvB

where v is speed = ? ( we need expression for this)

Volume V = AL ( area * length_

from Ohms law V = iR

and as R = rho L/A

V = i rho L/A

L v B = i rho L/A

v = rho i /A B

speed v = rho * D* AL /AB * LB

v = rho* D/B^2

v = 1.7e -8 * 9 e 3 /(0.09* 0.09)

v = 0.0188 m/s

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