Question

Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, 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. 1:02
• D. $\sqrt{3}:1$

Answer 1

Answer: (A)

$1:\sqrt{2}$

Answer 2

Suppose the magnetic field produced due to each coil is $B$.
The two coils are kept perpendicular hence, the angle between these is $90^{\circ}$ therefore, the resultant magnetic field is given by
$=\sqrt{B^{2}+B^{2}+2 B. B. \cos 90^{\circ}}$
$=\sqrt{2 B^{2}+2 B^{2} \times 0}$
$=\sqrt{2 B^{2}}=B \sqrt{2}$
Hence, the ratio of magnetic field due to one coil and the resultant magnetic field is given by
$=\frac{B}{\sqrt{2 B}}=1: \sqrt{2}$