Two concentric co-planar coils of turns and n, have radii ratio $2 : 1$ respectively. Equal current in both the coil flows in opposite direction. If net magnetic field is zero at their common centre then $n_{1} : n_{2}$ . is:

2:1

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1:2

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1:1

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4:1

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Solution

The correct option is D 2:1
Given: $\frac{r_{1}}{r_{2}} = \frac{2}{1}$ ,equal current
Solution: Formula of magnetic field at the centre of current carrying coil is:
$B = \frac{μ_{0} n i}{2 r}$
If the B=0 then $\frac{μ_{0} n_{1} i}{2 r_{_{1}}} = \frac{μ_{0} n_{2} i}{2 r_{_{2}}}$
$\frac{r_{1}}{r_{2}} = \frac{n_{1}}{n_{2}} = \frac{2}{1}$
Hence the correct answer is A

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