Question

Two similar coils are kept mutually perpendicular such that their centers coincide. At the center, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown:

• A. $ 1:\sqrt{2} $
• B. $ 1:2 $
• C. $ 1:3 $
• D. $ \sqrt{3}:1 $

Answer 1

Answer: (A)

When the two coils are kept perpendicular to each other, then resultant field in one coil is directed along the axis of coil and the other downwards, hence resultant field is

$B'=\sqrt{B^{2}+B^{2}}=\sqrt{2 B}$
Ratio of magnetic field due to one coil and resultant is
$\frac{B}{B \sqrt{2}}=\frac{1}{\sqrt{2}}$