Question

A long wire is known to have a radius greater than 4.0 mm and to carry a current uniformly distributed over its cross section. if the magnitude of the magnetic field is 0.285 mt at a point 4.0 mm from the axis of the wire and 0.200 mt at a point 10 mm from the axis, what is the radius of the wire?

Answer 1

Magnetic field outside it due to long wire is given by

$B = \frac{u_o i}{2 \pi r}$

Magnetic field due to long wire inside wire at any point

$B = \frac{u_o i r}{2 \pi R^2}$

Now the ratio of two magnetic field is given by

$\frac{B_{in}}{B_{out}} = \frac{r_1/R^2}{1/r_2}$

$\frac{0.285}{0.200} = \frac{4*10}{R^2}$

$1.425 = \frac{40}{R^2}$

R = 5.3 mm