Question

If the ratio of magnetic fields at two points in a definite direction due to a long current carrying wire is $\frac{3}{4},$ then the ratio of the distances of these points from the wire will be :

• A. $\frac{2}{\sqrt{3}}$
• B. $\frac{4}{3}$
• C. $\sqrt{\frac{3}{4}}$
• D. $\sqrt{\frac{3}{2}}$

Answer 1

The correct option is B $\frac{4}{3}$

Given:

$\frac{B_1}{B_2}=\frac{3}{4}$


$\because$ Magnetic field due to long current carrying wire is given by

$B=\frac{{\mu }_{0}i}{2\pi r}$

$\therefore B\propto \frac{1}{r}$

Or , $\frac{B_1}{B_2}=\frac{r_2}{r_1}$

$\Rightarrow \frac{r_2}{r_1}=\frac{3}{4}\text{or}\frac{r_1}{r_2}=\frac{4}{3}$

Hence, option (b) is the correct answer.