An ideal long solenoid of radius is wound with turns per metre and carries a steady…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

The Boundary-Value Problem, Ch The vector potential and the magnetostatic boundary-value problem

Problem

An ideal long solenoid of radius

a = 2.0\,\mathrm{cm}

is wound with

n = 1.0\times10^4

turns per metre and carries a steady current

I = 5.0\,\mathrm{A}

. Take the axis along

\hat{\mathbf{z}}

and use the azimuthal vector potential

\mathbf{A} = A_\phi(s)\hat{\boldsymbol{\phi}}

s

being the distance from the axis. ((a)) Find the field

B

inside the solenoid. ((b)) Find

A_\phi

s = 1.0\,\mathrm{cm}

, inside the winding. ((c)) Verify by taking the curl in cylindrical coordinates that this

\mathbf{A}

reproduces

B\hat{\mathbf{z}}

at that point.