Discussion Forum

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)

Answer:

Explanation:

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