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Two circular coils A and B with their Centre’s laying on the same axis have same number of turns and carryequal currents in the same sense. They are separated by a distance, have different diameters but subtend same solid angle at a point P lying on their common axis. The coil B lies exactly midway between coil A and the point P. The magnetic field at point P due to coils A and B are B₁ and B₂ respectively.Then select the wrong statements .

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$B_{1} > B_{2}$

$B_{1} < B_{2}$

$\frac{B_{1}}{B_{2}} = 2$

$\frac{B_{1}}{B_{2}} = \frac{1}{2}$

answer is A, C.

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Detailed Solution

$B = \frac{μ_{0} {NIr}^{2}}{2 {(r^{2} + x^{2})}^{3 / 2}} along X -axis$

$\Rightarrow B = \frac{μ_{0} NI}{2 r} \frac{r^{3}}{{(r^{2} + x^{2})}^{\frac{3}{2}}}$

Now $x_{1} = 2 x_{2} a n d r_{1} = 2 r_{2} . W h i c h g i v e s B_{2} = 2 B_{1} .$

$\Rightarrow \frac{B_{1}}{B_{2}} = \frac{r_{2}}{r_{1}} = \frac{1}{2} \Rightarrow \frac{B_{1}}{B_{2}} = \frac{r_{2}}{r_{1}} = \frac{1}{2}$

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