# Physics Class 12 NCERT Solutions: Chapter 5 Magnetism and Matter Part 4

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Q: 10. A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at with the horizontal. The horizontal component of the earth’s magnetic field at the place is known to be. Determine the magnitude of the earth’s magnetic field at the place.

Horizontal component of earth’s magnetic field,

Angle made by the needle with the horizontal plane Angle of dip

Earth’s magnetic field strength

We can relate and as:

Hence, the strength of earth’s magnetic field at the given location is.

Q: 11. At a certain location in Africa, a compass points west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points above the horizontal. The horizontal component of the earth’s field is measured to be. Specify the direction and magnitude of the earth’s field at the location.

Angle of declination,

Angle of dip,

Horizontal component of earth’s magnetic field,

Earth’s magnetic field at the given location

We can relate and as:

Earth’s magnetic field lies in the vertical plane, West of the geographic meridian, making an angle of (upward) with the horizontal direction. Its magnitude is.

Q: 12. A short bar magnet has a magnetic moment of. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

Magnetic moment of the bar magnet,

(a) Distance,

The magnetic field at distance d, from the centre of the magnet on the axis is given by the relation:

Where,

Permeability of free space

The magnetic field is along the direction.

(B) The magnetic field at a distance of on the equatorial line of the magnet is given as:

The magnetic field is along the direction.

Q: 13. 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 from the centre of the magnet. The earth’s magnetic field at the place is 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 from the centre of the magnet? (At null points, field due to a magnet is equal and opposite to the horizontal component of earth’s magnetic field.)

Earth’s magnetic field at the given place,

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

Where,

Permeability of free space

Magnetic moment

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

[Using equation (i)]

Total magnetic field,

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

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