In Fig. 28-47, 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 approximately zero to its maximum value of approximately 4.0cm, the magnitude τof the torque on the loop changes. The maximum value of τis localid="1662889006282">4.80×10-8N.m . What is the current in the loop?

Short Answer

Expert verified

The current in the loop is, i = 0.0030 A

Step by step solution

01

Given

The maximum torque on the loop isτ=4.80×10-8Nm

The maximum possible length of loop L = 4.0 cm = 0.04 m

Magnetic field, B = 0.040 T

02

Understanding the concept

We use the equation of torque acting on a current loop. By using this equation and considering the maximum area of loop (as the maximum torque is given), we can calculate the current in a loop.

Formulae:

τ=NiABsinθA=side2

03

Calculate the current in a loop

The maximum possible length of a loop is 0.04 cm.

So, the length of wire will be approximately 0.08 cm.

Now, the equation for a torque on a current loop is

τ=NiABsinθ

We can see that the torque on a current loop can be maximum when area of loop A is maximum.

For the rectangular loop, the maximum area is obtained when it becomes a square.

So, if we make the 8.0 cm wire in a square shape, the side of square will be

side=14×0.08=0.02m

So, the area of square is

A=side2=0.022=0.0004m2

Now, rearranging the equation of torque for current and substituting the value of A, we get

i=τNABsinθi=4.80×10-81×0.0004×0.04×sin90oi=3.00×10-3A=0.0030A

Hence, the current in the loop is, i = 0.0030 A

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