Question

A long, straight wire of radius R carries a steady current I that is uniformly distributed through the cross section of the wire. Calculate the magnetic field a distance r from the center of the wire in regions r ≥ R and r < R.

Answer 1

a

When
`r \ge R`

`B = ( \mu_o * I)/( 2 \pi r )`

b

When
`r< R`

`B = [(\mu_o * I )/( 2 \pi R^2) ]* r`

Step-by-step explanation:

From the question we are told that

The radius is R

The current is I

The distance from the center

Ampere's law is mathematically represented as

`B[2 \pi r] = \mu_o * (I r^2 )/(R^2 )`

`B = ( \mu_o)/(2 \pi ) * (r)/(R^2)`

When
`r \ge R`

=>
`B = ( \mu_o * I)/( 2 \pi r )`

But when
`r< R`

`B = [(\mu_o * I )/( 2 \pi R^2) ]* r`