The ratio of magnetic fields due to a bar magnet at the two axial points P 1 and P 2 which are separated from each other by 10 cm is 25 : 2 . P 1 Point is situated at 10 cm from the centre of the magn

Question

The ratio of magnetic fields due to a bar magnet at the two axial points P 1 and P 2 which are separated from each other by 10 cm is 25 : 2 . P 1 Point is situated at 10 cm from the centre of the magnet. (Points P 1 and P 2 are on the same side of magnet and distance of P 1 and P 2 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

TestHub · Accepted Answer

B 1 B 2 = 25 2 μ 0 4 π M d 1 ( d 1 2 − l 2 ) 2 μ 0 4 π M d 2 ( d 2 2 − l 2 ) 2 = 25 2 d 1 d 2 × ( d 2 2 − l 2 ) 2 ( d 1 2 − l 2 ) 2 = 25 2 d 1 = 10 c m , d 2 = 20 c m 10 20 × ( 20 2 − l 2 10 2 − l 2 ) 2 = 25 2 400 − l 2 = 5 ( 100 − l 2 ) 4 l 2 = 100 ⇒ l 2 = 25 l = 5 c m

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