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Question

(a) Deduce the expression for the potential energy of a system of two charges q1 and q2 located r1 and r2, respectively, in an external electric field.
(b) Three point charges, + Q + 2Q and - 3Q are placed at the vertices of an equilateral triangle ABC of side l. If these charges are displaced to the mid-point A1,B1 and C1, respectively, find the amount of the work done in shifting the charges to the new locations.
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Solution
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(a)(i) work done to bring a charge q in the electric field at a distance r1=q1V(r1)
(ii) work done to bring a charge q in the electric field at a distance r2=q2V(r2)
(iii) work done on q2 to move it against the force of q1=Kq1q2r12
The potential energy of the system =q1V(r1)+q2(V)(r2)+Kq1q2r12
(b) work done in moving charges = Potential of the initial position - Potential of the final position.
Now, Potential of the initial system =V12+V23+V31=2KQ2+(3KQ2)+(6KQ2)=7KQ2J
potential energy after moving to position, A1,B1&C1
=K(2Q)(Q)1/2+K(Q)(3Q)1/2+K(3Q)(2Q)1/2
=4KQ26KQ212KQ2=14KQ2J
work done =7Q2K(14KQ2)=7KQ2J

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(b) Three point charges, + Q + 2Q and - 3Q are placed at the vertices of an equilateral triangle ABC of side l. If these charges are displaced to the mid-point A1,B1 and C1, respectively, find the amount of the work done in shifting the charges to the new locations.
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