Question

A circular loop of radius 'a' is carrying a current 'i'. At a point P on its axis, the magnetic field will be proportional to?
Given: P is X units away from the centre of the loop and x >>> a.

• A. $\frac{1}{x^2}$
• B. $\frac{1}{x^3}$
• C. x
• D. $\frac{1}{x}$

Answer 1

The correct option is B $\frac{1}{x^3}$

The field at axial point due to a ring is given by,
$|\overrightarrow{B}|=\frac{{\mu }_{0}i{a}^2}{2(a^2+x^2{)}^{3/2}}$
$=\frac{{\mu }_{0}i{a}^2}{2x^3{(\frac{a^2}{x^2}+1)}^{3/2}}$
if x >>> a
$\Rightarrow \frac{a^2}{x^2}\to 0$
$|\overrightarrow{B}|=\frac{{\mu }_{0}i{a}^2}{2x^3}\Rightarrow |\overrightarrow{B}|\alpha \frac{1}{x^3}$