Three rings, each having radius R, are placed mutually perpendicular to each other and each having its centre at the origin of co-ordinate 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.
`thereforevecB_("net")=(mu_(0)i)/(2R)(hati+hatj+hatk)rArrB_("net")=sqrt3(mu_(0)I)/(2R)`