-cass wehave shown that the force on a closed current loop in a uniform magnetic

Question

-cass wehave shown that the force on a closed current loop in a uniform magnetic field is zero. Will i still be true if the magnetic field is not uniform and changes from point to point? Try figure this out in the example below. A long,straight wire is in pl ane of a rectangular loop as shown. The task is to find the overall force on a closed loop: (a) Compute the force on side AB. (b) Compute the force on side CD (c) What is the net force on the sides perpendicular to the wire and why? (d) What is the net force on the loop? Let a 2.0 cm, b-1.2m,x 6.0 cm, and the current in both the wire and the loop is 30 A. You can use the fact that the magnitude of B from a wire is given by B = , where .-4x-10" Tm/A.

Explanation / Answer

a] F = ibB = i2*b*u0i1/[2pi a] = 30*1.2*2e-7*30/0.02 = 0.0108 N upward

b]F = ibB = i2*b*u0i1/[2pi x] = 30*1.2*2e-7*30/0.06 = 0.0036 N downward

c] Net force will be 0 N as force on them will cancel because of opposite direction.

d] Net force = 0.0108 - 0.0036 = 0.0072 N upward

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