First slide

Magnetic field due to a current carrying circular ring

Question

A and B. are two centric circular conductor of centre O and carrying currents i₁ and i₂, as shown in fig.
The ratio of their radii is 1:2 and ratio of the flux densities at O due to A and B is 1 :3. The value of i₁, / i,₂will be

Easy

A

1/6
B

1/4
C

1/2
D

1/3

Solution

Here, $B_{1} = \frac{μ_{0} i_{1}}{2 r_{1}} and B_{2} = \frac{μ_{0} i_{2}}{2 r_{2}}$
$∴ \frac{B_{1}}{B_{2}} = \frac{i_{1}}{r_{1}} \times \frac{r_{2}}{i_{2}} = \frac{i_{1}}{i_{2}} \times \frac{r_{2}}{r_{1}}$
or $\frac{i_{1}}{i_{2}} = \frac{B_{1}}{B_{2}} \times \frac{r_{1}}{r_{2}} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

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