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

Explanation

Magnetic field induction due to vertical loop at the centre O, is
`B_(1)=(mu_(0)I_(1))/(2R)=(mu_(0))/(10^(-1))( :.R=5 cm)`
Magnetic field induction due to horizontal loop at the centre O is,
`B_(2)=(mu_(0)I_(2))/(2R)=(3mu_(0))/(10^(-1))`
`:. B_(1) and B_(2)` are perpendicular to each other, therefore the resultant magnetic field induction at the centre O is,
`B_("net") = sqrt(B_(1)^(2)+B_(2)^(2))`
`=sqrt(((4mu_(0))/(10^(-1)))^(2)+((3mu_(0))/(10^(-1)))^(2))`
`=50xx4pixx 10^(-7)=62.8xx10^(-6)T=62.8muT`
Direction of resultant magnetic field,
`"tan" theta=(B_(2))/(B_(1))=(3mu_(0)xx10^(-1))/(4mu_(0)xx10^(-1))`
or `"tan" theta= (3)/(4) or, theta ~~ 37^(@)`
Resulting magnetic field B make an angle `37^(@)` with `B_(1)`.