Question

The ratio of magnetic fields due to a bar magnet at the two axial points P₁ and P₂ which are separated from each other by 10 cm is 25 : 2. Points P₁ is situated at 10 cm from the centre of the magnet. Magnetic length of the bar magnet is ______.

(Points P₁ and P₂ are on the same side of magnet and distance of P₂ from the centre is greater than distance of P₁ from the centre of magnet)

Options

• 5 cm

• 10 cm

• 15 cm

• 20 cm

Answer 1

The ratio of magnetic fields due to a bar magnet at the two axial points P₁ and P₂ which are separated from each other by 10 cm is 25 : 2. Points P₁ is situated at 10 cm from the centre of the magnet. Magnetic length of the bar magnet is 5 cm.

Explanation:

According to question,

`"B"_1/"B"_2=25/2` ⇒ `(mu_0/(4pi)("Md"_1)/(("d"_1^2-"l"^2)^2))/(mu_0/(4pi)("Md"_2)/(4pi("d"_2^2-"l"^2)))=25/2`

`"d"_1/"d"_2xx(("d"_2^2-"l"^2)^2)/(("d"_1^2-"l"^2)^2)=25/2`

d₁ = 10 cm, d₂ = 20 cm

`10/20xx((20^2-"l"^2)/(10^2-"l"^2))=25/2`

400 - l² = 5(100 - l²)

4l² = 100 ⇒ t² = 25 or, l = 5 cm