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 0.040 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 appsoximately zero to its maximum value of approximately 4.0 cm, the magnitude of the torque on the loop changes. The maximum value of the torque is 4.8 x 10 ^ -8 Nm. What is the current in the loop when the torque is at its maximum value?

Explanation / Answer

torque on loop is given By T = NIAB sin theta

where I = cuurnet

A = area

N = no. of tunrs

B = magnetic field

theta = 90

here Length L (2* (a+b) = 0.04m

a+b = 0.02 m

area of square = 0.02*0.02 = 4*10^-4

so rearaniugnthe terms

I = T/(NABsin theta)

I = 4.8*10^-8/( 1* 0.04*4*10^-4* 0.04)

I = 75 mA

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