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,
[tex]r_B=R[/tex]
And [tex]r_A=R/2[/tex]
We know that the magnetic field at a distance R is inversely proportional to the distance from wire as :
[tex]B=\dfrac{\mu_o}{2\pi}\dfrac{I}{r}[/tex]
[tex]B_A\propto\dfrac{1}{(R/2)}[/tex]
[tex]B_B\propto\dfrac{1}{(R)}[/tex]
[tex]\dfrac{B_A}{B_B}=\dfrac{1/(R/2)}{1/R}[/tex]
[tex]\dfrac{B_A}{B_B}=\dfrac{2}{1}[/tex]
[tex]B_A=2B_B[/tex]
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.
