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Electrostatic Potential And Capacitance

Question
CBSEENPH12039553
Wired Faculty App

The electrostatic potential inside a charged spherical ball is given by Φ = ar2 + b where r is the distance from the centre; a,b are constants. Then the charge density inside the ball is

  • -6aε0r

  • -24πaε0

  • -6aε0

  • -24πaε0r

Solution

C.

-6aε0

Electric field, 
straight E space equals space minus space dϕ over dt space equals space minus space 2 ar By space Gauss apostrophe straight s space theorem comma straight E space left parenthesis 4 πr squared right parenthesis space equals space straight q over straight epsilon subscript 0 straight q space equals space minus 8 πε subscript 0 ar squared Now comma space the space charge space density comma space straight rho space equals space straight q over straight v space equals space fraction numerator negative 8 πε subscript 0 ar cubed space over denominator begin display style 4 over 3 end style πr squared end fraction space equals space minus 6 straight epsilon subscript 0 straight a

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