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

Options

A. `sqrt3(mu_0I)/(2R)`
B. zero
C. `(sqrt2-1) (mu_0I)/(2R)`
D. `(sqrt3-sqrt2) (mu_0I)/(2R)`

Answer

A

Explanation

(a) `vecB=(mu_0I)/(2R)(+-hati)+(mu_0I)/(2R)(+-hatj)+(mu_0I)/(2R)(+-hatk)`
`|vecB|=(mu_0I)/(2R)(sqrt3)`