# Solved Problems-5

Problem-5

(a) A magnetic field is given in cylindrical coordinates by

where,
A rectangular plane is located in the yz-plane and parallel to the z-axis as shown in the figure. The loop is moving in the plane with a velocity where

(b) Also, find the circulation of induced electric field around the loop, if the loop is moving in the plane with a velocity and if the magnetic field is given by
where, , and are constants.

*B*_{0}is a constant*v*_{0}is a constant. Find the circulation of induced electric field around the loop.(b) Also, find the circulation of induced electric field around the loop, if the loop is moving in the plane with a velocity and if the magnetic field is given by

**Rectangular loop moving in a magnetic field**

Solution

(a) Since the loop is moving and the magnetic field is constant, the circulation of induced electric field around the loop is,

where

*c*is an arbitrary constant.When

*r*â†’*y*, it results,(b) Here, since the magnetic field is also time varying, in addition to the component of (a), another component will be as given.

*r*â†’

*y*, it results,