Two identical loops P and Q each of radius `5cm` are lying in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net field at the common centre of the two coils, if they carry currents equal to `3A` and `4A` respectively.

Answer

`6*28xx10^-5T`; Direction can not be determined as direction of current is not given

Explanation

`B_P=(mu_0I_1)/(2r)=((4pixx10^-7)xx3)/(2xx(5xx10^-2))=12pixx10^-6T`
`B_Q=(mu_0I_2)/(2r)=((4pixx10^-7)xx4)/(2xx(5xx10^-2))=16pixx10^-6T`
Net magnetic field
`B=sqrt(B_P^2+B_Q^2)`
`=sqrt((12pixx10^-6)^2+(16pixx10^-6)^2)`
`=4pixx10^-6sqrt(9+16)=(4pixx10^-6)xx5`
`=20xx3*14xx10^-6T=6*28xx10^-5T`
The direction of current I is not given, hence, direction of `vecB` cannot be predicted.