Two identical short bar magnets, each having magnetic moment `M`, are placed a distance of `2d` apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

Options

A. `(mu_(0))/(4pi)(sqrt(2))""(M)/(d^(3))`
B. `(mu_(0))/(4pi)(sqrt(3))""(M)/(d^(3))`
C. `((2mu_(0))/(pi))(M)/(d^(3))`
D. `(mu_0)/(4pi)(sqrt(5))""(M)/(d^(3))`

Answer

D

Explanation

At point P net magnetic field `B_("net")=sqrt(B_(1)^(2)+B_2^(2))`

where , `B_(1)=(mu_(0))/(4pi)*(2M)/(d^(3))`
` and B_(2)=(mu_(0))/(4pi)*(M)/(d^(3))`
`implies B_("net")=(mu_(0))/(4pi)*(sqrt(5)M)/(d^(3))`