The ratio of magnetic fields due to a bar magnet at the two axial point P1 and P2 which are separated from each other by 10 cm is 25; 2 point P1 is situated at 10 cm from the centre of the magnet. The magnetic length  of the bar magnet is (point P1 and P2  are o2n the same side  of magnet and distance of P2 from the centre is greater than the distance of P1  from the centre of the magnet)

A) 5 cm

B) 10 cm

C) 15 cm

D) 20 cm


Option B


Let magnetic field at P1 is B1 and at P2 is B2


$\therefore$    $\frac{B_{1}}{B_{2}}=\frac{\frac{x_{1}}{(x_{1}^{2}-l^{2})^{2}}}{\frac{x_{2}}{(x_{2}^{2}-l^{2})^{2}}}=\frac{(x_{2}^{2}-l^{2})^{2}}{(x_{1}^{2}-l^{2})^{2}}\times\frac{x_{1}}{x_{2}}$

$\Rightarrow$     $\frac{25}{2}=\frac{10}{20}\left[\frac{x_{2}^{2}-l^{2}}{x_{1}^{2}-l^{2}}\right]^{2}$

or   $\left[\frac{x_{2}^{2}-l^{2}}{x_{1}^{2}-l^{2}}\right]=5$

 or $x_{2}^{2}-l^{2}=5x_{1}^{2}-5l^{2}$

 or  $ 4l^{2}=5x_{1}^{2}-5x_{2}^{2}$

  = 5 x (10)2-(20)2

 = 500-400=100

 $\Rightarrow$   $ l^{2}=25$

$\Rightarrow$   l=5 cm

 $\therefore$   2l=10 cm