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. P1 Point is situated at 10 cm from the centre of the magnet. (Points P1 and P2 are on the same side of magnet and distance of P1 and P2 from the centre of magnet is much greater than the distance of two ends of the magnet from the centre). Magnetic length of the bar magnet is

MHT CET · Physics · Magnetic Properties of Matter

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 $25 : 2$ . P₁Point is situated at $10 cm$ from the centre of the magnet. (Points P₁ and P₂are on the same side of magnet and distance of P₁ and P₂from the centre of magnet is much greater than the distance of two ends of the magnet from the centre). Magnetic length of the bar magnet is

A $5 cm$
B $10 cm$
C $15 cm$
D $20 cm$

Verified Solution

Answer & Solution

Correct Answer

(B) $10 cm$

Step-by-step Solution

Detailed explanation

\frac{B_{1}}{B_{2}} = \frac{25}{2}

\frac{\frac{μ_{0}}{4 π} \frac{M d_{1}}{{(d_{1}^{2} - l^{2})}^{2}}}{\frac{μ_{0}}{4 π} \frac{M d_{2}}{{(d_{2}^{2} - l^{2})}^{2}}} = \frac{25}{2}

\frac{d_{1}}{d_{2}} \times \frac{{(d_{2}^{2} - l^{2})}^{2}}{{(d_{1}^{2} - l^{2})}^{2}} = \frac{25}{2}

d_{1} = 10 c m, d_{2} = 20 c m

\frac{10}{20} \times {(\frac{20^{2} - l^{2}}{10^{2} - l^{2}})}^{2} = \frac{25}{2}

400 - l^{2} = 5 (100 - l^{2})

4 l^{2} = 100 \Rightarrow l^{2} = 25

l = 5 c m

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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