For the arrangement shown in Fig. determine the magnetic field at centre O.

Explanation

Let current flowing through coil 1 be `i_1` and through coil 2 be `i_2`.

Radius of each coil=R. Hence, magnetic field at O due to coil
1 is
`vecB_1=(mu_0i_1)/(2R) hati`
and magnetic field at O due to coil 2 is
`vecB_2=(mu_0i_2)/(2R) hatj`
Therefore, net megnetic field `vecB=vecB_1+vecB_2`
` implies vecB=(mu_0i_1)/(2R) hati+(mu_0i_2)/(2R) hatj`
` implies |vecB|=(mu_0)/(2R) sqrt(i_1^2+i_2^2)`