Physics Class 12 NCERT Solutions: Chapter 4 Moving Charges and Magnetism Part 4

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Magnetic field of a current loop equation

Magnetic Field of a Current Loop Equation

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Q: 12. In Exercise (Reference: Ch. 4 Moving Charges And Magnetism Part 3) obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

Answer:

Magnetic field strength,

Charge of the electron,

Mass of the electron,

Velocity of the electron,

Radius of the orbit,

Frequency of revolution of the electron

Angular frequency of the electron

Velocity of the electron is related to the angular frequency as:

In the circular orbit, the magnetic force on the electron is balanced by the centripetal force. Hence, we can write:

This expression for frequency is independent of the speed of the electron.

On substituting the known values in this expression, we get the frequency as:

Hence, the frequency of the electron is around 18 MHz and is independent of the speed of the electron.

Q: 13. (A) A circular coil of turns and radius carrying a current of is suspended vertically in a uniform horizontal magnetic field of magnitude. The field lines make an angle of with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.

(b) Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

Answer:

(A) Number of turns on the circular coil,

Radius of the coil,

Area of the coil

Current flowing in the coil,

Magnetic field strength,

Angle between the field lines and normal with the coil surface,

The coil experiences a torque in the magnetic field. Hence, it turns. The counter torque applied to prevent the coil from turning is given by the relation,

(b) It can be inferred from relation (i) that the magnitude of the applied torque is not dependent on the shape of the coil. It depends on the area of the coil. Hence, the answer would not change if the circular coil in the above case is replaced by a planar coil of some irregular shape that encloses the same area.

Q: 14. Two concentric circular coils X and Y of radii and, respectively, lie in the same vertical plane containing the north to south direction. Coil X has turns and carries a current of; coil Y has turns and carries a current of. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

Answer:

Radius of coil

Radius of coil Y,

Number of turns of on coil

Number of turns of on coil

Current in coil

Current in coil

Magnetic field due to coil X at their centre is given by the relation,

Where,

Magnetic field due to coil Y at their centre is given by the relation,

Hence, net magnetic field can be obtained as: