An ideal solenoid of radius a has n turns per unit length and current I. The magnetic flux Φ_B 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 A) . B) . C) μ₀πa²nI. D) 2μ₀πa²nI. E) 0.

Question

Quizplus · Accepted Answer

The magnetic field inside a solenoid is given by B = μnI, where n is the number of turns per unit length and I is the current. At a point inside the solenoid that is offset from the axis by a distance r, the field is given by B = μnIr/2a. At the surface of the solenoid, r = a, so B = μnI/2. 
The magnetic flux through an area A is given by Φ = BAcosθ, where θ is the angle between the field and the area. In this case, the area is at a 45° angle to the axis, so cosθ = 1/√2. The area is a circle with radius a, so its area is πa^2. Putting it all together, we get Φ = μnaIa^2/2√2. 
Therefore, the correct answer is C.

An Ideal Solenoid of Radius a Has N Turns Per