Question

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

A
+7.62×102 J
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B
7.62×102 J
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C
2×102 J
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D
0.1 J
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Solution

## The correct option is B −7.62×10−2 JGiven q1=1μ C , q2=2μ C , q3=−3μ C , q4=4μ C To find the electrical potential energy of a system of charges, we make pairs. If there are total n charges then total number of pairs are n(n−1)2. Electric potential energy for four point charges q1 , q2 , q3 and q4 would be given by, U=14πε0[q4q3r43+q4q2r42+q4q1r41+q3q2r32+q3q1r31+q2q1r21] .......(1) From the diagram we can deduce that, r41=r43=r32=r21=1 m and r42=r31=√(1)2+(1)2=√2 m Substituting the given data in equation (1) we get, U=9×109×10−6×10−6[4×(−3)1+4×2√2+4×11+(−3)×21+(−3)×1√2+2×11] ⇒U=9×10−3[−12+5√2]=−7.62×10−2 J Hence, option (b) is the correct answer.

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