Question

A current filament carrying 8 A in the a_z direction lies along the entire z axis in free space. A rectangular loop connecting A(0,0.2,0) to B(0,0.2,0.3) to C(0,0.7,0.3) to D(0,0.7,0) to A lies in the x = 0 plane. The loop current is 3 mA and it flows in the a_z direction in the AB segment.

(a) Determine F on side AB.

(b) Determine F on side DA.

(c) Determine the total force F_total on the loop.

Answer 1

---------------Solution of Part (a) -----------------------------------

To solve this problem first we have to calculate the strength of magntic field on Side AB due to current filament having 8A current by

and using this B we can find the Force on different sides by

So strength of magnetic field on the side AB =

This magnetic field will be in negative X direction (-X)

This force will be in _Y direction

---------------Solution of Part (b) -----------------------------------

Similarlly for DA we can calculae the B

Since in this case the distance from the wire is not fix so the magnetic field will be changing throughout the lin DA and Force on this length is given by

This force will be in negative Z direction

---------------Solution of Part (c) -----------------------------------

Total force on the loop will be Zero since all force are cancelling each other.