An ideal solenoid of radius a has n turns per unit length and current I.The magnetic flux $\phi$B through any area completely inside the solenoid, centred on the solenoid axis but at a 45$\degree$ angle to the axis, so that it touches the inside of the solenoid, as shown below, is:
C)($\mu$0 $\pi$a2nI.)
D)2$\mu$0 $\pi$a2nI.
E)0.

Question

An ideal solenoid of radius a has n turns per unit length and current I.The magnetic flux $\phi$B through any area completely inside the solenoid, centred on the solenoid axis but at a 45$\degree$ angle to the axis, so that it touches the inside of the solenoid, as shown below, is: 
C)($\mu$0 $\pi$a2nI.) 
D)2$\mu$0 $\pi$a2nI. 
E)0.

Quizplus · Accepted Answer

Inside the solenoid, the magnetic field is given by B = μ₀nI, where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. At 45 degrees to the axis, the magnetic flux through a circular area of radius a is φ = Bπa²cos45 = (√2/2)μ₀nIa²π. Therefore, the answer is C, (μ₀nIa²π).

An Ideal Solenoid of Radius a Has N Turns Per ϕ\phiϕ

An Ideal Solenoid of Radius a Has N Turns Per $\phi$