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.

$1 : \sqrt{2}$

1:3

1:2

$\sqrt{3} : 1$

Solution

$1 : \sqrt{2}$

Suppose magnetic field is produced due to each coil is B.The coils are kept perpendicular hence, the angle between these is 90⁰.

Therefore the resultant magnetic field is given by : $\frac{B}{\sqrt{2 B}} = 1 : \sqrt{2} Hence the ratio of magnetic field is due to one coil and the resultant magnetic field is given by = \sqrt{B^{2} + B^{2} + 2 B . B \cos 90^{0}} = \sqrt{2 B^{2} + 2 B^{2} \times 0} = \sqrt{2 B^{2}} = B \sqrt{2}$

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Electromagnetic Induction

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.

$1 : \sqrt{2}$

1:3

1:2

$\sqrt{3} : 1$

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Electromagnetic Induction

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. 1:2 1:3 1:2 3:1

Some More Questions From Electromagnetic Induction Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.

$1 : \sqrt{2}$

1:3

1:2

$\sqrt{3} : 1$