An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux ΦB through any area completely inside the solenoid, centered on the solenoid axis but at a 45° angle to the axis so that it touches the inside of the solenoid as shown below, is

Question

An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux ΦB through any area completely inside the solenoid, centered on the solenoid axis but at a 45° angle to the axis so that it touches the inside of the solenoid as shown below, is ​  ​

Quizplus · Accepted Answer

The magnetic field inside an ideal solenoid is given by B = μ0nI, where n is the number of turns per unit length and I is the current. Since the area in question is completely inside the solenoid, the magnetic field is uniform and perpendicular to the area, so we can use the equation ΦB = BA, where A is the area. The area in question is a circle of radius a and angle 45°, so its area is 1/8 of the total circular area with radius a. Therefore, A = πa^2/8. Combining these equations, we get ΦB = BA = μ0πa^2nI/8, which is choice C.

An Ideal Solenoid of Radius a Has N Turns Per