Two concentric coils each of radius equal to ( 2 cm ) are placed right angles to each other. If ( 3 ~A ) and ( 4 ~A ) are the currents flowing through the two coils respectively. The magnetic induction (in ( Wb m ⁻² ) ) at the centre of the coils will be

Step-by-step solution

Magnetic induction at the centre of coil is given as [ B= ₀ 2 I a ] where ( a ) is radius of coil. Here, ( a=2 cm =2 10⁻² ~m ) For current [ I₁=3 A, B₁= ₀ 2 3 2 10⁻² =3 10⁻⁵ T ] For current [ I₂=4 A, B₂= ₀ 2 4 2 10⁻² =4 10⁻⁵ ~T ] Then, magnetic induction at centre of coils is [ B= B₁ ²+B₂ ² = (3 10⁻⁵ )²+ (4 10⁻⁵ )² =5 10⁻⁵ ~T ]