Two identical coils P and Q each of radius R are lying in perpendicular planes such that they have a common centre. Find the magnitude and PC direction of the magnetic field at the common centre of the two coils, if they carry currents equal to land `sqrt3 I` respectively.

Explanation

Magnetic field at the centre of current carrying loop P is given by :
`B_(1) = (mu_(0)I)/(2 pi R) ` , vertically upwards
Magnetic field at the centre of current carrying loop Q is given by :
`B_(2) = (mu_(0) sqrt 3I)/(2 pi R) `, towards left
Net magnetic field at the common centre of loops will be :
`B_("net") = sqrt(B_(1)^(2)+B_(2)^(2)) = sqrt(((mu_(0)I)/(2 pi R))^(2) + ((mu_(0)sqrt3 I)/(2 pi R))^(2))`
` = (mu_(0)I)/(2 piR) sqrt4 = (mu_(0)I)/(pi R) `
Direction of magnetic field will be :
` tan theta = B_(1)/B_(2) = 1/sqrt3`
` theta = 30^(@)` .