Question

The magnetic induction at a point near a current carrying conductor is doubled when current through it is changed and the point is shifted so that its distance is 2/3rd of the original distance. The ratio of the current is :

• A. 2:1
• B. 3:4
• C. 1:2
• D. 4:3

Answer 1

The correct option is B 3:4

The magnetic induction at a distance $r$ from a conductor carrying current $I_1$ is,

$B=\frac{{\mu }_0{I}_1}{2\pi r}$

The magnetic induction at a distance $2/3r$ from a conductor carrying current $I_2$ is $2B$

$2B=\frac{{\mu }_0{I}_2}{2\pi 2/3r}$

Divide the above equation, we get

$\frac{I_1}{I_2}=\frac{3}{4}$

$I_1:I_2=3:4$