Question

A circular coil of radius 3R is carrying current. The ratio of magnetic fields at centroid of coil and at a point distance 4R from center of coil (point is on the axis of coil)

• A. $\frac{125}{27}$
• B. $\frac{125}{64}$
• C. $\frac{64}{27}$
• D. $\frac{64}{125}$

Answer 1

The correct option is A $\frac{125}{27}$

$\frac{B_C}{B_P}=\frac{\frac{{\mu }_{0}i}{2R}}{\frac{{\mu }_0}{4\pi }\frac{2M}{(R^2+x^2{)}^{\frac{3}{2}}}}=\frac{i}{2R}\frac{\frac{}{4\pi (R^2+x^2{)}^{\frac{3}{2}}}}{2M}$$=\frac{i\pi }{Ri\pi R^2}(R^2+x^2{)}^{\frac{3}{2}}$
$=\frac{(R^2+x^2{)}^{\frac{3}{2}}}{R^2}$
$={\left(\frac{R^2+x^2}{R^2}\right)}^{\frac{3}{2}}$
$={\left(\frac{9R^2+16R^2}{9R^2}\right)}^{\frac{3}{2}}={\left(\frac{25}{9}\right)}^{\frac{3}{2}}$
$=\frac{125}{27}$