Question

If in a circular coil $A$ of radius $R,$ current $i$ is flowing and in another coil $B$ of radius $2R$ , a current $2i$ is flowing, then the ratio of the magnetic fields, $B_{A}$ and $B_{B}$ produced by them at their centres will be:

• A. $1$
• B. $2$
• C. $\frac{1}{2}$
• D. $4$

Answer 1

Answer: (A)

Magnetic field in circular coil $A$ is
Similarly, $B_{A}=\frac{\mu _{0} N i}{2 R}$
$R$ is radius and $i$ is current flowing in coil.
$B_{B}=\frac{\left(\mu \right)_{0} N \left(\right. 2 i \left.\right)}{2 \, . \left(\right. 2 R \left.\right)}$
$ \, =\frac{\mu _{0} N i}{2 R}$
$\frac{B_{A}}{B_{B}}=\frac{1}{1}=1$