# Physics Class 12 NCERT Solutions: Chapter 5 Magnetism and Matter Part 7

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Q: 19. A telephone cable at a place has four long straight horizontal wires carrying a current of in the same direction east to west. The earth’s magnetic field at the place is, and the angle of dip is. The magnetic declination is nearly zero. What are the resultant magnetic fields at points below the cable?

Number of horizontal wires in the telephone cable,

Current in each wire,

Earth’s magnetic field at a location,

Angle of dip at the location,

Angle of declination,

For a point 4 cm below the cable:

Distance,

The horizontal component of earth’s magnetic field can be written as:

Where,

Magnetic field at due to current in the four wires

Permeability of free space

The vertical component of earth’s magnetic field is given as:

The angle made by the field with its horizontal component is given as:

The resultant field at the point is given as

For a point 4 cm above the cable:

Horizontal component of earth’s magnetic field:

Vertical component of earth’s magnetic field:

And resultant field:

Q: 20. A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of turns and radius. The coil is in a vertical plane making an angle of with the magnetic meridian. When the current in the coil is, the needle points west to east.

(A) Determine the horizontal component of the earth’s magnetic field at the location.

(B) The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of 90º in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.

Number of turns in the circular coil,

Current in the coil,

Angle of dip,

(a) The magnetic field due to current I, at a distance r, is given as:

Where,

Permeability of free space

The compass needle points from West to East. Hence, the horizontal component of earth’s magnetic field is given as:

(B) When the current in the coil is reversed and the coil is rotated about its vertical axis by an angle of, the needle will reverse its original direction. In this case, the needle will point from East to West.

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