Question

A single-turn square loop of side L is centered on the axis of a long solenoid. In addition, the plane of the square loop is perpendicular to the axis of the solenoid. The solenoid has 1490 turns per meter and a diameter of 6.00 cm, and carries a current of 2.46 A. Find the magnetic flux through the loop in each of the following.
a) L = 3cm
b) L = 6cm
c) L = 12cm

I found a to be 4.15e-6, b to be 1.66e-5 and c to be 6.63e-5, but only a is right. the answers are within ten percent of 1.2e-5 and are the same answer but I can't find what they should be. Please someone help soon.

Answer 1

Hmmm. A is right, you say.

The area of L^2 in a is 9cm^2
the area of the solenoid is 9PI

Area outside the solenoid does not contain the inner field.

b. Flux=4.15E-6* 9PI/9=4.15E-6*PI=1.304E-5

That is 8 percent higher than 1.2E-5

Now, larger L does not contain any more flux, as the flux is contained within the solnoid

Think about this, I may not be understanding the problem.