Question

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?

Answer 1

Explanation:

It is given that, there are two points 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 such that,

$r_B=R$

And $r_A=R/2$

We know that the magnetic field at a distance R is inversely proportional to the distance from wire as :

$B=\dfrac{\mu_o}{2\pi}\dfrac{I}{r}$

$B_A\propto\dfrac{1}{(R/2)}$

$B_B\propto\dfrac{1}{(R)}$

$\dfrac{B_A}{B_B}=\dfrac{1/(R/2)}{1/R}$

$\dfrac{B_A}{B_B}=\dfrac{2}{1}$

$B_A=2B_B$

So, the magnetic field at point A larger than the magnetic field at point B by a factor of 2. Hence, this is the required solution.