Three rings, each having equal radius R, are placed mutually perpendicular to each other and each having its centre at the origin of coordinate system. If current I is flowing through each ring, then the magnitude of the magnetic field at the common centre is

Explanation

`B` due to the ring lying in `XY-` plane is
`B_(xy)=(mu_(0)I)/(2R)`along `Z-` axis.
`B` due to the ring lying in `YZ-` plane is `B_(yz)=(mu_(0)I)/(2R)` along `X-` axis and `B` due to the ring lying in `XZ-` plane is `B_(xz)=(mu_(0)I)/(2R)` along `Y-` axis.
`:. vec(B)_(n et)=(mu_(0)I)/(2R)(hat(i)+hat(j)+hat(k))impliesB_(n et)=sqrt(3)(mu_(0)I)/(2R)`