#### Question

Two identical circular coils, P and Q each of radius R, carrying currents 1 A and √3A respectively, are placed concentrically and perpendicular to each other lying in the XY and YZ planes. Find the magnitude and direction of the net magnetic field at the centre of the coils.

#### Solution

Magentic field at the centre of the coil are perpendicular to each other. Therefore net magnetic field (*B*) is the resultant of the two fields caused due to coil P and Q, respectively.

`B_P = (μ_oI)/(2πR)= (μ_o)/(2πR)`

`B_Q= (μ_oI)/(2πR)= (μ_osqrt3)/(2πR)`

Net magnetic field, `B = sqrt(B_P^2 + B_Q^2)`

`=sqrt((μ_o/(2πR))^2 + ( (μ_osqrt3)/(2πR))^2) `

`= μ_o/(2πR)sqrt4`

`= μ_o/(πR)`

**For direction of net magnetic field**

`tanβ =(AB)/(BC)`

`= (μ_o/(2πR))/((μ_osqrt3)/(2πR)) = 1/sqrt3`

`β= 30^@`

The direction of net magnetic field is 30° with the X-direction.