A short bar magnet with its north pole facing north forms a neutral point at `P` in the horizontal plane. If the magnet is rotated by `90^(@)` in the horizontal plane, the net magnetic induction at `P` is (Horizontal component of earth's magnetic field `=B_(H))`

Options

A. `0`
B. `2B_(H)`
C. `sqrt(5)/2B_(H)`
D. `sqrt(5) B_(H)`

Answer

D

Explanation

Initially

neutral point obtained on equatoria line and at neutral point `|B_(H)|=|B_(e)|`
where `B_(H)= `Horizontal component of earth's magnetic field, `B_(e)=` Magnetic field due to bar magnet on its equatorial line

Finally
Point `P` comes on axial line of the magnet and at `P`, net magnetic field `B=sqrt(B_(a)^(2)+V_(H)^(2))`
`=sqrt((2B_(e))^(2)+(B_(H))^(2))=sqrt((2B_(e))^(2)+B_(H)^(2))=sqrt(5) B_(H)`