Question

The magnetic induction due to a current $i$ passed in a straight conductor at a distance $d$ from it is proportional to

• A. $\frac{1}{d}$
• B. $\frac{1}{d^2}$
• C. $d$
• D. $d^2$

Answer 1

Answer: (A)

$\frac{1}{d}$

According to Ampere's law, magnetic induction due to a current i passed in a straight conductor at a distance d from it is $\oint B.dl={\mu }_{0}i$
$B\oint dl={\mu }_{0}i$
$B\left(2\pi d\right)={\mu }_{0}i$
$B=\frac{{\mu }_{0}i}{2\pi d}$
$\Rightarrow B\propto \frac{1}{d}$