Question

A conductor is made in the form of a hollow cylinder with inner and outer radii a and b, respectively. It carries a current I, uniformly distributed over its cross section. Part A Derive an expression for the magnitude of the magnetic field in the region r

Answer 1

Answer with Explanation:

We are given that

Inner radius,
`r_1=a`

Outer radius,
`r_2=b`

Current=I

a.If r<a

Consider a loop of radius r where r<a

Then, current enclosed by loop=
`I'=0`

Magnetic field,B=0

b.if a<r

Then,
`I'=I((r^2-a^2))/(b^2-a^2)`

`B=(\mu_0I')/(2\pi r)=(\mu_0I(r^2-a^2))/(2\pi r(b^2-a^2))`

c.r>b

Then,
`I'=I`

Magnetic field,
`B=(\mu_0I)/(2\pi r)`