Electrostatics 2 Question 2

2. A system of three charges are placed as shown in the figure

(Main 2019, 9 April I)

If D»d, the potential energy of the system is best given by

(a) 14πε0q2d+2qQdD2

(b) 14πε0+q2d+qQdD2

(c) 14πε0q2dqQd2D2

(d) 14πε0q2dqQdD2

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Answer:

Correct Answer: 2. (d)

Solution:

  1. The system of two charges, i.e. +q and q that are separated by distance d can be considered as a dipole. Thus, the charge Q would be at D distance from the centre of an electric dipole on its axial line.

So, the total potential energy of the system will be due to two components.

(1) Potential energy of dipole’s own system

q++q(PE)1=Kq1q2d=Kq2d

(2) Potential energy of charge Q and dipole system

(PE)2=KQqD2d

Hence, total potential energy of the system

(PE)total =(PE)1+(PE)2=Kq2dKQqD2d(PE)total =14πε0q2d+QqdD2



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