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Electrostatic Potential And Capacitance

Question
CBSEENPH12039282

A point charge +Q is placed at point O as shown in the figure. Is the potential
difference VA – VB is positive, negative or zero?

Solution

Electric potential at a distance r from the point charge +Q is given by, 
 V thin space left parenthesis straight r right parenthesis space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction space. space Q over r 
Potential at point A is, 

straight V space left parenthesis straight r subscript straight A space right parenthesis thin space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction space straight Q over straight r subscript straight A 
Similarly, potential at point B is given by, 
straight V space left parenthesis straight r subscript straight B space right parenthesis thin space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction space straight Q over straight r subscript straight B
Since rA < rB 

rightwards double arrow space straight V subscript straight A space greater than space straight V subscript straight B

therefore space straight V subscript straight A space minus space straight V subscript straight B space greater than thin space 0

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