Question

In each of the following situations, a coil rotates in a uniform magnetic field. Rank the coils in order of the maximum value of the alternating emfinduced in the coil, from greatest value to smallest value.

(i) A coil with 500 turns and area 2.00 * 10^–3 m² rotates at 50.0 rad/s in a magnetic field of magnitude 5.00 * 10^–3 T.

(ii) A coil with 400 turns and area 2.00 * 10^–3 m² rotates at 70.0 rad/s in a magnetic field of magnitude 5.00 * 10^–3 T.

(iii) A coil with 500 turns and area 3.00 * 10^–3 m² rotates at 50.0 rad/s in a magnetic field of magnitude 4.00 * 10^–3 T.

(iv) A coil with 800 turns and area 3.00 * 10^–3 m² rotates at 30.0 rad/s in a magnetic field of magnitude 3.00 * 10^–3 T.

Question 5 options:

	(iii) > (ii) > (i) > (iv)
	(iii) > (iv) > (ii) > (i)
	(iv) > (ii) > (i) >(iii)
	(ii) > (iii) > (i) > (iv)

Answer 1

Induced EMF is given by:

EMF = -N*d/dt

= Magnetic flux through loop = B.A = B*A*cos (wt)

w = angular frequency of rotation

N = number of loops

So,

EMF = -N*d(B*A*cos (wt))/dt

EMF = -N*B*A*d(cos (wt))/dt

EMF = -N*B*A*(-w*sin (w*t))

EMF = N*B*A*w*sin (w*t)

Now we know that maximum value of sine function is 1, So maximum induced emf will be:

EMF_max = N*B*A*w

Part (i) Using given values:

EMF_max = 500*5.00*10^-3*2.00*10^-3*50.0

EMF_max = 0.25 V

Part (ii) Using given values:

EMF_max = 400*5.00*10^-3*2.00*10^-3*70.0

EMF_max = 0.28 V

Part (iii) Using given values:

EMF_max = 500*4.00*10^-3*3.00*10^-3*50.0

EMF_max = 0.30 V

Part (iv) Using given values:

EMF_max = 800*3.00*10^-3*3.00*10^-3*30.0

EMF_max = 0.216 V

Correct order will be:

(iii) > (ii) > (i) > (iv)

Correct option is A.