The figure given below shows four arrangements of charged particles, all at the same distance from the origin. Rank the situation according to the net electric potential $(V_{1}, V_{2}, V_{3}, V_{4})$ at the origin, most positive first

V_{1} > V_{2} > V_{3} > V_{4}

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V_{2} > V_{1} > V_{3} > V_{4}

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V_{2} > V_{1} > V_{4} > V_{3}

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V_{4} > V_{1} > V_{3} > V_{2}

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Solution

The correct option is C $V_{2} > V_{1} > V_{4} > V_{3}$
let $r$ be the same distance for all charges.
$V_{1} = k (2 q / r - 9 q / r) = - 7 k q / r$
$V_{2} = k (- 2 q / r - 3 q / r) = - 5 k q / r$
$V_{3} = k (- 2 q / r - 2 q / r - 3 q / r - 2 q / r) = - 9 k q / r$
$V_{4} = k (- 6 q / r + q / r - 5 q / r + 2 q / r) = - 8 k q / r$
Thus, $V_{2} > V_{1} > V_{4} > V_{3}$

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The figure given below shows four arrangements of charged particles, all at the same distance from the origin. Rank the situation according to the net electric potential (V1,V2,V3,V4) at the origin, most positive first

The correct option is C V2>V1>V4>V3let r be the same distance for all charges.V1=k(2q/r−9q/r)=−7kq/rV2=k(−2q/r−3q/r)=−5kq/rV3=k(−2q/r−2q/r−3q/r−2q/r)=−9kq/rV4=k(−6q/r+q/r−5q/r+2q/r)=−8kq/rThus, V2>V1>V4>V3

The figure given below shows four arrangements of charged particles, all at the same distance from the origin. Rank the situation according to the net electric potential $(V_{1}, V_{2}, V_{3}, V_{4})$ at the origin, most positive first