Question

Considering magnetic field due to a circular loop of radius R along the axis of it, approximately at what distance from the center of the loop the field is $\frac{1}{2\sqrt{2}}$ times of its value at the center?

• A. $4R$
• B. $R$
• C. $3R$
• D. $6R$

Answer 1

Answer: (B)

$R$

$\text{Solution}:$

$B_{axis}=\frac{{\mu }_{0}I{R}^2}{2(R^2+x^2{)}^{3/2}}$

=$\frac{{\mu }_{0}I}{2R}\times \frac{1}{(1+\frac{x^2}{R^2}{)}^{3/2}}$

Also,

$B_{centre}=\frac{{\mu }_{0}I}{2R}$

$⟹B_{axis}=\frac{B_{centre}}{(1+\frac{x^2}{R^2}{)}^{3/2}}=\frac{B_{centre}}{2\sqrt{2}}$

$\therefore$$(1+\frac{x^2}{R^2}{)}^{3/2}$= $2\sqrt{2}$

$⟹x=R$

$\text{Hence B is the correct option}$