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Current Loop Is a Magnet?

Two concentri...

Question

Two concentric circular loops of radii $r_{1}$ and $r_{2}$ , carry clockwise and anticlockwise current $i_{1}$ and $i_{2}$ ,. If the centre is a null point , $i_{1} / i_{2}$ must be equal to

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Solution

Given,

At the center they have equal magnitude of magnetic field in opposite direction.

$| B_{1} | = | B_{2} |$

$\frac{μ i_{1}}{2 r_{1}} = \frac{μ i_{2}}{2 r_{2}}$

$\frac{i_{1}}{i_{2}} = \frac{r_{1}}{r_{2}}$

Hence, $\frac{i_{1}}{i_{2}} = \frac{r_{1}}{r_{2}}$

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