Question

Two similar coils of radius R are lying concentrically with their planes at right angles to each other.The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the centre will be

Answer 1

The net magnetic field at the common center due the two mutually perpendicular coils is equal to √5μI/2R.

Magnetic field at the center due to the first coil is B1 = μI/2R

​

Magnetic field at the center due to the second coil which is perpendicular to the first coil is B2 = μ(2I)/2R

​

Hence net magnetic field at the center = √((B1)² + (B2)²)

=> √((μI/2R)² + (μ(2I)/2R)²)

=> √5μI/2R

Answer 2

The resultant magnetic field induction at the center will be √(5)(μ₀I)/(2R)

Explanation:

From question, the magnetic field (B) at the center of the circular current carrying coil of radius R and current I.

The magnetic field is given by the formula:

B = (μ₀I)/(2R)

If the current though the coil is 2I, then magnetic field becomes,

B = (μ₀2I)/(2R)

B = 2 (μ₀I)/(2R) = 2B

The resultant magnetic field is:

Br = √B² + (2B)²

Br = √(5B²)

Br = √(5)B

∴ Br = √(5)(μ₀I)/(2R)