Question

Two very long solenoids have the same number of turns per unit length, and carry the same current, but the radius of the cross-section of solenoid #1 is twice that of solenoid #2. How do the magnetic field fluxes through the solenoids compare?

Select the best answer.

Select the best answer.

	The flux through solenoid #2 is twice the flux through solenoid #1.
	They are equal.
	The flux through solenoid #1 is twice the flux through solenoid #2.
	The flux through solenoid #1 is four times the flux through solenoid #2

Answer 1

The best answer is option (d)The flux through solenoid #1 is four times the flux through solenoid #2.

Explanation:

It is stated in the question that the solenoids have got same length L, current I and no of turns n.

we know that, the field of a long solenoid is given by:

B = K o N/L x I

As all the variables are same for both the solenoids, so we conclude that the magnetic field for both the solenoids will be the same.

Let 1 be the flux of solenoid 1 and 2 be that of 2.

We know that, the flux is given by:

= B.A where B is the magnetic field and A is the area of cross section.

Its given that, r1 = 2 r2

1 = B A1 = B pi (r1)² = B pi (2 r2)²   

1 = B pi 4 r2²   eq(1)

2 = B A2 = B pi r2² eq(2)

Divide (1)/(2)

1/2 =   B pi 4 r2² /   B pi r2²   

1/2 = 4

1 = 4 2

Hence, The flux through solenoid #1 is four times the flux through solenoid #2.