Two points, point a and point b, are situated above a current-carrying wire. point b is located at a distance r from the wire, which is twice as far from the wire as point a. by what factor is the magnetic field at point a larger or smaller than the magnetic field at point b?

By a factor of 2

Explanation:

The strength of the magnetic field produced by a current-carrying wire is given by

where

is the vacuum permeability

I is the current

r is the distance  from the wire

At point A, which is located at a distance from the wire, the magnetic field strength is

Point B is located at a distance of

from the wire, so the strength of the field at point B is

Or equivalently,

So, the field at A is twice as strong as the field at B.