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)`
`impliesB_("net")=mu_(0)/(4pi).(sqrt(5)M)/d^(3)`