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. `sqrt(3)(mu_(0)I)/(2R)`
B. Zero
C. `(sqrt(2)-1)(mu_(0)I)/(2R)`
D. `(sqrt(3)-sqrt(2))(mu_(0)I)/(2R)`

Answer

A

Explanation

Magnetic field at centre of current carrying ring is: `B=(mu_(0)i)/(2R)`
Direction of field will be orthogonal vector at centre irrespective of direction of current in rings.
`B_("Net")=sqrt(((mu_(0)i)/(2R))^(2)+((mu_(0)i)/(2R))^(2)+((mu_(0)i)/(2R))^(2))=sqrt(3)(mu_(0)i)/(2R)`