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 = (u_o i)/(2 \pi r)`

Magnetic field due to long wire inside wire at any point

`B = (u_o i r)/(2 \pi R^2)`

Now the ratio of two magnetic field is given by

`(B_(in))/(B_(out)) = (r_1/R^2)/(1/r_2)`

`(0.285)/(0.200) = (4*10)/(R^2)`

`1.425 = (40)/(R^2)`

R = 5.3 mm