A rectangular loop carrying current lies in the plane of a uniform magnetic fiel

Question

A rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.0315 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 2.62 cm, the magnitude of the torque on the loop changes. The maximum value of is 3.99 × 10-8 N*m. What is the current in the loop?

Explanation / Answer

We know that the torque is given by T=IA*B*Sin(theta)

Assuming theta to be 90 degrees. T=IA*B

Now Given that maximum torque =3.99*10^-8 Nm

Since only A is varying in this expression of torque and we know that torque will be maximum when A will be maximum which will be in case of a square formed by the wire.

So Area=(.0262*.0262)m^2

A=6.82*10^-4 m^2

So, 3.99*10^-8=I*6.82*10^-4*.0315

I=1.857*10-3 Amps

I=1.87 mA

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