Problem 7: A 0.2 m wire is bent into a circular shape and is placed in a uniform magnetic field of 2 T. If the current in the wire is 20 mA, then find the maximum torque acting on the loop.

Solution

Given                         Length of the wire = L = 0.2 m                B = 2 T                  Current = I = 20 mA = 20 * 10^-3A

Required                   Torque = τ =?

Strategy: Since τ = IBA, where A is area of the loop. We do not know the area of the circular shape therefore, first we find it.

When the 0.2 m long wire is bent in a circular shape, the circumference of the shape will also be 0.2 m. Therefore, apply formula C = 2πr to find radius of the circle.

Now area of a circle is = πr², therefore,

Put this value (of area) in the formula for torque, given above,