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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 7.62×102 J
Given

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(n1)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=9×109×106×106[4×(3)1+4×22+4×11+(3)×21+(3)×12+2×11]

U=9×103[12+52]=7.62×102 J

Hence, option (b) is the correct answer.

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