Question

The ratio of magnetic fields on the axial line of a long magnet at distance of 10cm and 20cm is 12.5.1. The length of the magnet is

Answer 1

Thus the length of the magnet is 10 m.

Explanation:

We are given that:

Magnetic field at an axial point

B  (a x i a l)  =  μ 0 /  4 π  x 2  M  d  (  d ^2  −  l^ 2 ) ^2

where  M  is the magnetic moment, d is the distance of the point from center of the magnet and  2 l  is the length of the magnet.

Substituting the values provided,

B 1  / B  2  =  d 1 /  d 2  x d 2^ 2  −  l ^2 ( d  1^2  −  l ^2  ) 2

⇒  12.5  / 1  =  10  / 20  ×  (  20 ^2 −  l^ 2  /  10 ^2  −  l^ 2 )^ 2

⇒  5  ×  ( 10 ^2  −  l^2 )

=  ( 20 ^2  −  l  2  )

⇒  l  =  5  

⇒  2  l  =  10

Thus the length of the magnet is 10 m.