Question

The magnetic field at the center of current carrying circular loop is $B_1$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_2$. The value of $B_1/B_2$ will

• A. $5:\sqrt{3}$
• B. $8:1$
• C. $12:\sqrt{5}$
• D. $9:4$

Answer 1

The correct option is B $8:1$

The magnetic field at the center of current carrying circular loop,

$B_1=\frac{{\mu }_{0}i}{2R}$

$B_2=\frac{{\mu }_{0}i{R}^2}{2(R^2+x^2{)}^{\frac{3}{2}}}$

$\Rightarrow \frac{B_1}{B_2}=\frac{1}{R^3}(R^2+x^2{)}^{\frac{3}{2}}$

$=\frac{1}{R^3}\left(8R^3\right)$

$\Rightarrow \frac{B_1}{B_2}=8$