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

Data
`(B_(1))/(B_(2))=(25)/(2) , r_(1) =10cm , r_(2) =20cm, 2l =?`
`B = (mu_(0))/(4pi) (2Mr)/((r^(2) -l^(2))^(2))b prop(r)/((r^(2)-l^(2))^(2))`
Now
`(B_(1))/(B_(2))= (r_(1)/((r_(1)^(2)-l^(2))^(2)))/((r_(2))/((r_(2)^(2)-l^(2))^(2)))=(r_(1))/((r_(1)^(2)-l^(2))^(2))xx((r_(2)^(2)-l^(2))^(2))/(r_(2))`
`therefore (25)/(2) =(10)/((100 -l^(2))^(2))xx((400-l^(2))^(2))/((100-l^(2))^(2))`
`5= (400-l^(2))/(100-l^(2))`
`therefore 400=l^(2) =500-5 l^(2)`
`4l^(2) =100`
`l^(2) =25`
`l=5`
`therefore 2l =10 cm`