Classical Electrodynamics · Problem 5.3

Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws — John David Jackson

Physics — E&M · finite-solenoid-axial-field

Problem

A right-circular solenoid of finite length

L

and radius

a

has

N

turns per unit length and carries a current

I

. Show that the magnetic induction on the cylinder axis in the limit

NL \to \infty

B_z = \frac{\mu_0 NI}{2}\,(\cos\theta_1 + \cos\theta_2)

where the angles are defined in the figure.