Question

Radius of current carrying coil is ${}^{\prime }{R}^{\prime }$. Then ratio of magnetic fields at the centre of the coil to the axial point, which is $R\sqrt{3}$ distance away from the centre of the coil is

• A. $1:1$
• B. $1:2$
• C. $1:4$
• D. $8:1$

Answer 1

The correct option is D $8:1$

Magnetic field at centre $B_{centre}=\frac{{\mu }_{o}i}{2R}$
Magnetic field at any distance $x$ from centre$B_{axial}=\frac{{\mu }_{o}i{R}^2}{2(x^2+R^2{)}^{\frac{3}{2}}}$

Here, $x=\sqrt{3}R$
Therefore,
$B_{axial}=\frac{{\mu }_{0}i{R}^2}{2(R^2+(\sqrt{3}R{)}^2{)}^{\frac{3}{2}}}$
So, the ratio is
$\frac{B_{centre}}{B_{axial}}=\frac{8}{1}=8:1$