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Electric Charges And Fields

Question
CBSEENPH12039525

This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this uniform charge distribution, there is a finite value of the electric potential at the centre of the sphere, at the
surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero.

Statement 1: When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by qρ/3εo
Statement 2: The electric field at a distance r(r < R) from the centre of the sphere is  ρr/3εo

  • Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

  • Statement 1 is true, Statement 2 is false

  • Statement 1 is false, Statement 2 is true

  • Statement 1 is true, Statement 2 is the correct explanation for statement 1

Solution

C.

Statement 1 is false, Statement 2 is true

contour integral straight E with rightwards arrow on top. straight d with rightwards arrow on top straight A space equals space 1 over straight epsilon subscript 0 open parentheses straight rho space straight x space 4 over 3 πr cubed close parentheses
straight E space equals space fraction numerator ρr over denominator 3 straight epsilon subscript 0 end fraction
Statement 2 is correct
increment PE space equals space left parenthesis straight V subscript sur minus straight V subscript cent right parenthesis straight q space equals space minus fraction numerator straight q over denominator 6 straight epsilon subscript 0 end fraction ρR squared
statement 1 is incorrect.