Three point charges q1=1μC,q2=−2μC and q3=3μC are placed at (1m,0,0) and (0,2m,0) and (0,0,3m) respectively. The electric potential at origin is
A
9×103J/C
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B
3×103J/C
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C
15×103J/C
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D
12×103J/C
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Solution
The correct option is A9×103J/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=1μC is at placed at (1m,0,0)
Therefore the distance of charge q1 from origin (0,0,0) is, r1=√(1−0)2+(0−0)2+(0−0)2 ∵[r=√(x2−x1)2+(y2−y1)2+(z2−z1)2]
or, r1=1m
similarly, q2=−2μC and r2=2m q3=3μC and r3=3m
From Eq. (i) the net potential at point P is, VP=9×109[1×10−61+(−2×10−6)2+(3×10−6)3] ∴VP=9×103J/C
Why this question?Concept: Distance between any two points A(x1,y1,z1)andB(x2,y2,z2)is given by r=√(x2−x1)2+(y2−y21)+(z2−z1)2