Question

Radius of a current carrying coil is $R$ The ratio of magnetic field at a axial point which is $R$ distance away from the centre of the coil to the magnetic field at the centre of the coil:

Answer 1

At centre

$\overrightarrow{B}=\frac{\mu {}_{o}i}{2R}$

At point $P$

$\overrightarrow{B}=\frac{{\mu }_{oi}{a}^2}{(a^2+d^2{)}^{3/2}}$

$a=R$

$d=R$

${\overrightarrow{B}}_1=\frac{{\mu }_{oi}{R}^2}{2(2R^2{)}^{3/2}}=\frac{{\mu }_{oi}}{R\left(2\right)\left(2^{3/2}\right)}$

$=\frac{{\mu }_{oi}}{R4\sqrt{2}}$

$\frac{\overrightarrow{B}}{{\overrightarrow{B}}_1}=2\sqrt{2}$