First slide

Magnetic field due to a current carrying circular ring

Question

A and B are two concentric circular conductors of centre O and carrying currents i₁ and i₂ as shown in the figure. If ratio of their radii is 1 : 2 and ratio of the flux densities at O due to A and B is 1 : 3, then the value of i₁/i₂ is

Easy

A

$\frac{1}{6}$
B

$\frac{1}{4}$
C

$\frac{1}{3}$
D

$\frac{1}{2}$

Solution

$\begin{array}{l} r_{1} : r_{2} = 1 : 2 and B_{1} : B_{2} = 1 : 3 . We know that \\ B = \frac{μ_{0}}{4 π} . \frac{2 πni}{r} \Rightarrow \frac{i_{1}}{i_{2}} = \frac{B_{1} r_{1}}{B_{2} r_{2}} = \frac{1 \times 1}{3 \times 2} = \frac{1}{6} \end{array}$

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