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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 −7.62×10−2 JPotential 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)(10−6)(10−6)[(4)(−3)1+(4)(2)√2+(4)(1)1+(−3)(2)1+(−3)(1)√2+(2)(1)1] U=(9.0×10−3)[−12+5√2] U=−7.62×10−2 J Hence, option (b) is the correct answer.

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