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Electrostatic Potential And Capacitance

Question
CBSEENPH12039843

The potential energy of a particle in a force field is,straight U space equals straight A over straight r squared minus straight B over straight r where A and B are positive constants are r is the distance of a particle from the centre of the field. For stable equilibrium, the distance of a particle is

  • B/2A

  • 2A/B

  • A/B

  • B/A

Solution

B.

2A/B

Given, the potential energy of particle in a force field
straight U space equals space straight A over straight r squared minus straight B over straight r to the power of 1
For space stable space equilibrium comma space straight F space equals space minus space dU over dr space equals space 0
0 equals negative fraction numerator 2 straight A over denominator straight r cubed end fraction space plus space straight B over straight r squared
Or
fraction numerator 2 straight A over denominator straight r end fraction space equals space straight B
The space distance space of space particle space from space the space centre space of space the space field
straight r equals space fraction numerator 2 straight A over denominator straight B end fraction

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