In the figure, a rectangular loop carrying current lies in the plane of a unifor

Question

In the figure, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.0366 T. The loop consists of a single turn of flexible conducting wire that is wrapped around a flexible mount such that the dimensions of the rectangle can be changed. (The total length of the wire is not changed.) As edge length x is varied from approximately zero to its maximum value of approximately 2.23 cm, the magnitude T of the torque on the loop changes. The maximum value of T is 3.15 times 10^- 8 N*m. What is the current in the loop? Number Units

Explanation / Answer

Uniform magnetic field, B =  0.0366 T

Maximum torque max = 3.15 X10-8 N*m

x = 0.0223 m

Perimeter of the loop is calculated by ,

P = 2(x+y) = 2 * 0.0223 m = 0.0446 m

For maximum area , we frame a square of side a =P/4 = 0.0115 m

Maximum torque is given by,

   max = BiA = Bia2

So Current is :

      i = max /Ba2 = 3.15 X10-8 / 0.0366 * ( 0.0115 )^2 = 6.5077 X 10-3 A

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