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. \(1:3\)
• D. \(\sqrt{3}:1\)

Hint:

When two vectors of equal magnitude are perpendicular, resultant magnitude = \(\sqrt{2}\) times each.

Answer 1

The Correct Option is A

Step 1: Concept:
Magnetic field at centre of a coil \(B = \frac{\mu_0 I}{2R}\). When two coils are perpendicular, resultant field is vector sum.
Step 2: Explanation:
Let \(B\) be field due to one coil. Since coils are perpendicular, fields are perpendicular to each other.
Resultant field = \(\sqrt{B^2 + B^2} = \sqrt{2}B\).
Ratio of field due to one coil to resultant = \(\frac{B}{\sqrt{2}B} = \frac{1}{\sqrt{2}}\).
Step 3: Conclusion:
Thus, ratio = \(1:\sqrt{2}\).