In the figure below a rectangular loop carrying current lies

In the figure below, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.045 T. The loop consists of a sing 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 >> ¦ changed.) As edge length x is varied from approximately rcro to its maximum value of approximately 4.6 cm, the magnitude r of the torque on the loop change The maximum value of tau Is 4.9 times 1o^-8 Nm. What Is the current In the loop?

Solution

uniform magnetic field B =  0.045 T, the maximum torque _max = 4.9X10^-8 N*m, and x =4.6*10^-2 m

the perimeter of the loop is,

      P = 2x+2y = 2*4.6 cm = 9.2 cm = 9.2*10^-2m

for getting the maximum area ,

we frame a square of side a =P/4 = 2.3 *10^-2 m

the maximum torque is

   _max = BiA = Bia²

hence, the current is,

      i = _max /Ba² = 4.9X10^-8 /0.045*( 2.3 *10^-2)^2 = 0.002 A = 2.00X10^-3 A