Electrostatics 2 Question 6

6. Four equal point charges Q each are placed in the xy-plane at (0,2),(4,2),(4,2) and (0,2). The work required to put a fifth charge Q at the origin of the coordinate system will be

(a) Q24πε0

(b) Q24πε01+13

(c) Q222πε0

(d) Q24πε01+15

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Answer:

Correct Answer: 6. (d)

Solution:

  1. The four charges are shown in the figure below,

Electric potential at origin (0,0) due to these charges can be found by scalar addition of electric potentials due to each charge.

V=KQr1+KQr2+KQr3+KQr4V=KQ12+12+120+120=KQ1+15V=KQ(5+1)5V

Now, if another charge Q is placed at origin, then work done to get the charge at origin

W=QV

By putting the value of V from Eq. (ii) in Eq. (iii), we get

or

W=KQ2(5+1)5JW=Q24πε01+15J



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