Question

The magnetic field at the center of a current carrying loop of radius $0.1m$ is $5\sqrt{5}$ times that at a point along its axis. The distance of this point from the center of the loop is

• A. $0.2m$
• B. $0.05m$
• C. $0.1m$
• D. $0.25m$

Answer 1

Answer: (A)

$0.2m$

Magnetic field at a point on the axis $B^{\prime }=\frac{{\mu }_{o}I{a}^2}{2(x^2+a^2{)}^{3/2}}$

where $a$ is the radius of the loop and $x$ is the distance of the point from the center of the loop.

Magnetic at the center of the loop $B_c=\frac{{\mu }_{o}I}{2a}$

Given : $B_c=5\sqrt{5}{B}^{\prime }$

$\therefore$ $\frac{{\mu }_{o}I}{2a}=5\sqrt{5}\times$ $\frac{{\mu }_{o}I{a}^2}{2(x^2+a^2{)}^{3/2}}$

Or $(\frac{x^2+a^2}{a^2}{)}^{3/2}=5^{3/2}$

Or $\frac{x^2+a^2}{a^2}=5$

Or $x^2=4a^2$

Or $x=2a$

Given : $a=0.1m$

$⟹$ $x=2\times 0.1=0.2m$