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Question

Three point charges q1=1 μC,q2=2 μC and q3=3 μC are placed at (1 m,0,0) and (0,2 m,0) and (0,0,3 m) respectively. The electric potential at origin is

A
3×103 J/C
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B
9×103 J/C
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C
12×103 J/C
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D
15×103 J/C
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Solution

The correct option is B 9×103 J/C
We know potential due to a system of point charges at any point P is given by,
VP = kq1r1+kq2r2+kq3r3 ....(i)

Here, q1=1 μC is at placed at (1 m,0,0)

Therefore the distance of charge q1 from origin (0,0,0) is,
r1=(10)2+(00)2+(00)2
[r=(x2x1)2+(y2y1)2+(z2z1)2 ]
or, r1=1 m
similarly, q2=2 μC and r2=2 m
q3=3 μC and r3=3 m
From Eq. (i) the net potential at point P is,
VP=9×109[1×1061+(2×106)2+(3×106)3]
VP=9×103 J/C

Why this question?Concept: Distance between any two points A(x1,y1,z1) and B(x2, y2, z2)is given by r=(x2x1)2+(y2y21)+(z2z1)2

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