The ratio of magnetic fields due to a bar magnet at the two axial points `P_(1) and P_(2)` which are separated from each other by 10 cm is 25 :2 . Point `P_(1)` is situated at 10 cm from the centre of the magnet. Magnetic length of the bar magnet is (Points `P_(1) and P_(2)` are on the same side of magnet and distance of `P_(2)` from the centre is greater than distance of `P_(1)` from the centre of magnet)

Options

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Answer

B

Explanation

Let magnetic field at `P_(1)` is `B_(1)` and at `P_(2)` is `B_(2)`

`:." "(B_(1))/(B_(2))=(x_(1)/(x_(1)^(2)-l^(2))^(2))/((x_(2))/((x_(2)^(2)-l^(2))^(2)))=((x_(2)^(2)-l^(2))^(2))/((x_(1)^(2)-l^(2))^(2))xx(x_(1))/(x_(2))`
`rArr" "(25)/(2)=(10)/(20)[(x_(2)^(2)-l^(2))/(x_(1)^(2)-l^(2))]^(2)`
`or" "[(x_(2)^(2)-l^(2))/(x_(1)^(2)-l^(2))]=5`
`or" "x_(2)^(2)-l^(2)=5x_(1)^(2)=5l^(2)`
`or" "4l^(2)=x_(1)^(2)-x_(2)^(2)`
`=xx(10)^(2)-(20)^(2)`
`=500-400=100`
`rArr" "l^(2)=25`
`rArr" "l=5cm`
`:." "2l=10cm`