The magnetic field 10 cm from a wire carrying a 1 a current is 2 μt. what is the field 4 cm from the wire? express your answer with the appropriate units.

Explanation:

We can solve the problem in two ways:

1) The magnetic field around a current-carrying wire is given by

where

is the permeabilty of free space

I is the current

r is the distance from the wire

Substituting I=1 A and , we find:

2) We can notice that the magnitude of the magnetic field around a current-carrying wire is inversely proportional to the distance from the wire:

which means that the product is constant if we keep the same wire. So we can write

and using we can find the magnetic field at 4 cm from the wire: