Question

A long wire is known to have a radius greater than 10.0 mm and less 20 mm, carry a current uniformly distributed over its cross section. If the magnitude of the magnetic field is 3 mT at a point 6.0 mm from the axis of the wire and 1.50 mT at a point 20 mm from the axis, what is the radius of the wire?

Answer 1

Radius = 7.75 mm

Step-by-step explanation:

magnetic field inside a point in the wire is given as

`B = (\mu_0 i r)/(2\pi R^2)`

now we have

`3mT = (\mu_0 i (6mm))/(2\pi R^2)`

now outside wire magnetic field is given as

`B = (\mu_0 i)/(2\pi r)`

now we have

`1.50 mT = (\mu_0 i)/(2\pi(20 mm))`

now divide above two equations

`2 = (6 mm* 20 mm)/(R^2)`

`R = 7.75 mm`