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

Step-by-step 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=(\mu_o)/(2\pi)(I)/(r)`

`B_A\propto(1)/((R/2))`

`B_B\propto(1)/((R))`

`(B_A)/(B_B)=(1/(R/2))/(1/R)`

`(B_A)/(B_B)=(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.