Question

Magnetic field at a distance $a$ from long current carrying wire is proportional to

• A. $\frac{1}{a}$
• B. $\frac{1}{a^2}$
• C. $\frac{1}{\sqrt{a}}$
• D. $\frac{1}{a^{3/2}}$

Answer 1

The correct option is A $\frac{1}{a}$

Applying Ampere's law on a loop of radius $a$ around the wire,

$\Rightarrow {\mu }_{0}I=B\left(2\pi a\right)$

$\Rightarrow B=\frac{{\mu }_{0}I}{2\pi a}$

$\Rightarrow B\propto \frac{1}{a}$