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Question:
A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. earths magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null-point (i.e., 14 cm) from the centre of the magnet? (At null points, field due to a magnet is equal and opposite to the horizontal component of earths magnetic field.)
Answer:

Earths magnetic field at the given place, H= 0.36 G

The magnetic field at a distance d, on the axis of the magnet is given as:

image084 NCERT Solutions class-12 physics Magnetism and Matter  …(i)

Where,

image009 NCERT Solutions class-12 physics Magnetism and Matter= Permeability of free space

M= Magnetic moment

The magnetic field at the same distance d, on the equatorial line of the magnet is given as:

image085 NCERT Solutions class-12 physics Magnetism and Matter  [Using equation (i)]

Total magnetic field,image086 NCERT Solutions class-12 physics Magnetism and Matter

image087 NCERT Solutions class-12 physics Magnetism and Matter

image088 NCERT Solutions class-12 physics Magnetism and Matter

Hence, the magnetic field is 0.54 G in the direction of earth’s magnetic field.

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