Physics Class 12 NCERT Solutions: Chapter 1 Electric Charges and Fields Part 3

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Dipole moment formula

Dipole Moment Formula

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Q: 9. A system has two charges and located at points respectively. What are the total charge and electric dipole moment of the system?

Answer:

Both the charges can be located in a coordinate frame of reference as shown in the given figure.

Q 9 The Charges Located in a Coordinate Frame of Reference

Q 9 the Charges Located in a Coordinate Frame of Reference

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At

At

Total charge of the system,

Distance between two charges at points A and B

Electric dipole moment of the system is given by,

Along positive z-axis

Therefore, the electric dipole moment of the system is along positive z-axis.

Q: 10. An electric dipole with dipole moment is aligned at with the direction of a uniform electric field of magnitude . Calculate the magnitude of the torque acting on the dipole.

Answer:

Electric dipole moment,

Angle made by with a uniform electric field,

Electric field,

The relation gives torque acting on the dipole is,

Therefore, the magnitude of the torque acting on the dipole is .

Q: 11. A polythene piece rubbed with wool is found to have a negative charge of .

(A) Estimate the number of electrons transferred (from which to which?)

(B) Is there a transfer of mass from wool to polythene?

Answer:

(A) When polythene is rubbed against wool, a number of electrons get transferred from wool to polythene. Hence, wool becomes positively charged and polythene becomes negatively charged.

Amount of charge on the polythene piece,

Amount of charge on an electron,

Number of electrons transferred from wool to polythene

can be calculated using the relation,

Therefore, the number of electrons transferred from wool to polythene is

(B) Yes

There is a transfer of mass taking place. This is because an electron has mass,

Total mass transferred to polythene from wool,

Hence, a negligible amount of mass is transferred from wool to polythene.