Two similar coils each of radius r and no. of turns n are lying concentrically with their planes at right angle to each other. The corrents folowing in them are 1 A and `sqrt3A` respectively. What is the magnetic field at centre of the coils ?

Options

A. `(mu_(0)n)/(2pir)`
B. `(mu_(0)n)/(sqrt3pir)`
C. `(mu_(o)n)/(r)`
D. `(sqrt3mu_(0)n)/(r)`

Explanation

The fields at the centres of the first and seocnd coils are given by
`B_(1) =(mu_(0))/(4pi) ((2pi n)/(r))" "because I_(1) =1A`
`and B_(2) =(mu_(0))/(4pi) ((2pi n xxsqrt3)/(r)) =sqrt3 B_(1)`
As the coils are at right angles, the directons of magnetic fields `B_(1) and B_(2)` will also be perpendicular to each other. `therefore` The resultant magnetic field
`B =sqrt(B_(1)^(2)+B_(2)^(2))=sqrt(B_(1)^(2) +(sqrt3B_(1))^(2))`
`=sqrt(4B_(1)^(2))=2B_(1)`
`therefore B = 2 xx (mu_(0))/(4pi) ((2pi n )/(r))therefore B =(mu _(0)n )/(r)`