4. A loop has a form of a square ofside a and it consists of N turns of wire. Th

Question

4. A loop has a form of a square ofside a and it consists of N turns of wire. The resistance of the wire is R. Magnetic field B is initially directed normally to the loop. Then the loop is rotated by 0 around some axis in its plane during the time At. What is the average EMF in the circuit? What is the average current? What is the charge that goes through the loop? What work Wshould be done to rotate the loop? Calculate the numerical value of W a cm, N 30, R 10 2, B 1 mT, 0 300, At-0.1 for 10 s. Do not calculate numerically any other quantities.

Explanation / Answer

Here values given to us are;

Magnetic field strength is B.

Length of loop is a.

Breadth of loop is a.

Area of loop, A = a2

No. of turns is N.

Initially angle between magnetic field and area vector is 0.

Finally the between magnetic field and area vector is .

Resistance of loop is R.

So

Initial magnetic flux, B = NA·B = NAB cos0 = Na2B

Final magnetic flux, B = NA·B = NAB cos = Na2B cos

So change in flux, = Na2B (cos - 1)

Induced e.m.f., e = -B/t = {Na2B (1 - cos)}/t =(Na2B/t)(1 - cos)

Induced current, i = e/R = (Na2B/t *R)(1 - cos).

So charge Q = i*t = (Na2B/R)(1 - cos).

Power generated, P = i2R ={N2a4B2)/(t)2*R}(1 - cos)2

So work done, W = P*t ={N2a4B2)/t*R}(1 - cos)2

Hence for given values, W = {(30)2(0.10)4(0.001)2)/(0.1)*(10)}(1 – cos30)2 = 1.615x10-9 J

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