a) Consider a rectangular loop of wire of width w and length l being pulled out

Question

a) Consider a rectangular loop of wire of width w and length l being pulled out of a region with a magnetic field B that is at right angles to the plane of the loop. Show that the loop is subject to a magnetic force F = B^2 w^2 v/R where R is the electrical resistance of the loop and v is the velocity with which it moves. Show in a diagram the direction of the force on the loop exerted by the magnetic field. b) Find the force per unit length with which two parallel wires a distance d apart carrying parallel currents attract each other. Suppose the wires are now immersed in water with a magnetic susceptibility of -0.9 times 10-5. Is the force per unit length changed? Is it increased or decreased? By what percentage is it changed?

Explanation / Answer

Given,

magnetic field B; width w, length L, resistance R, velocit v,

The induced emf in the loop from Faraday's law will be given by:

e = -d(phi)/dt = d(BA)/t = BdA/dt = B (w l)/t

from the defination of speed,

v = x/t = l/t

e = B w v

induced current in the loop will be:

i = e/R = B w v/R

We know that the force on the wire in magnetic field if given by:

F = B i w

putting the value of i in the expression of F

F = B (B w v/R) w = B^2 w^2 v/R

Hence, F = B^2 w^2 v/R

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