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Question

Four charges q1=1 μC, q2=2 μC, q3=3 μC and q4=4 μC are kept on the vertices of a square of side 1 m. Find the electric potential energy stored in this system of charges.


A
3.6×102 J
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B
7.62×102 J
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C
7.62×102 J
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D
3.6×102 J
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Solution

The correct option is B 7.62×102 J
Potential energy of the system of four charges is given by:

U=k[q4 q3r43+q4 q2r42+q4 q1r41+q3 q2r32+q3 q1r31+q2 q1r21] ....(1)

Given , r41=r43=r32=r21=1 m

and r42=r31=(1)2+(1)2=2 m

Substituting the given values with sign in equation (1), we get

U=(9.0×109)(106)(106)[(4)(3)1+(4)(2)2+(4)(1)1+(3)(2)1+(3)(1)2+(2)(1)1]

U=(9.0×103)[12+52]

U=7.62×102 J

Hence, option (b) is the correct answer.

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