Question

# Derive an expression for magnetic field at a point on the axial line of a bar magnet.

Hard
Solution
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## Let be a bar magnet of magnetic length and having each pole of magnetic strength . O is the center of magnet and is a point on axial line at a distance from the center of magnet , at which magnetic field has to be measured .The magnetic field at due to pole of magnet ,or     (along PX) .......................eq1And , the magnetic field at due to pole of magnet ,or     (along PS) ......................eq2Therefore , resultant magnetic field at point ,         (-ive sign is due to opposite directionS of and )It is clear from eq1 and eq2 that ,therefore the direction of   will be along .or         (alongPX)or         (alongPX)Now , (magnetic dipole moment of magnet)Hence ,     (alongPX)

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