Two short bar magnets A and B of dipole moment `0.15 Am^(2)` respectively are placed with their axes along the same line, with their centres 0.15 m apart. The dipole moments due to A and B point in opposite directions. What is the position of the point, between the two magnets, where the resultant induction is zero?

Options

A. 10 cm from the centre of A
B. 12 cm from the centre of A
C. 5 cm from the centre of A
D. 8 cm from the centre of A

Answer

C

Explanation

At point P, the magnetic inductions due to A and B are equal and opposite. Hence their resultant is zero.
`:' B_(1)=B_(2)` (in magnitude)
`:. mu_(0)/(4pi) (2M_(1))/d_(1)^(3)=mu_(0)/(4pi) (2M_(2))/((0.15-d_(1))^(3))`
`:. 0.15/d_(1)^(3)=1.2/((0.15-d_(1))^(3))`
`:. 1/d_(1)^(3)=8/((0.15-d_(1))^(3))`
`:. 8d_(1)^(3)=(0.15-d_(1))^(3)`
`:.` Taking cube roots of both sides, we get
`2d_(1)=0.15-d_(1) :. 3d_(1)=0.15 :. d_(1)=0.05 m=5` cm
`:.` P is at a distance of 5 cm from the centre of A.