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 0.0434 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 3.22 cm, the magnitude ? of the torque on the loop changes. The maximum value of ? is 5.11

In the figure, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.0434 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 3.22 cm, the magnitude ? of the torque on the loop changes. The maximum value of ? is 5.11 ? 10-8 N*m. What is the current in the loop?

Explanation / Answer

apply Torque T = NiAB sin theta

here No. of turns N = 1

current i =

A = area = lxb = 0.0322*0.0322 = 0.00103684 m^2

B = magnetic field = 0.00434

so   current i = T/(NABsin theta)

i = 5.11e-8/(1 * 0.00103684* 0.00434* sin 90)

i = 11.35 mA

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