A circular loop of radius a is placed in a diverging magnetic field B such that the angle between the normal to the plane of the loop and field anywhere on the loop is θ. Also, the magnetic field present is such that the lines cut the loop at 900. Derive an expression for the net force exerted by the field on the loop when a current i is made to flow through the loop.

 

Asked by Topperlearning User | 28th Apr, 2015, 02:05: PM

Expert Answer:

Let us consider an infinitesimal segment of the loop of length ds.

The magnetic field is perpendicular to all the segments of the loop.

Force on this segment, dF = iBds

Horizontal component of the force, dFH = (iB cosθ)ds

This component of the force points away from the loop.

Vertical component of the force, dFv = (iB sinθ)ds

This component of the force points upward from the plane of the loop.

When we sum each of these components for all segments of the loop, the sum of horizontal component of the force vanishes. This happens because  the horizontal force acting on the diametrically -opposite segments of the loop cancel each other out. As a result, only the vertical component of the force contributes to the net force on the loop.

The vertical component, which points upward, is

Fv = iB begin mathsize 11px style sin space straight theta integral ds end style = (2Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.a)iB sinθ (Since i,B, θ are constants)

 

Answered by  | 28th Apr, 2015, 04:05: PM