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Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance1 Mark
MCQ
The electrostatic potential on the surface of a charged conducting sphere is 100V. Two statments are made in this regard:
S1 : At any point inside the sphere, electric intensity is zero.
S2 : At any point inside the sphere, the electrostatic potential is 100V.
Which of the following is a correct statement?
  • A
    S1 is true but S2 is false.
  • B
    Both S1 & S2 are false.
  • C
    S1 is true, S2 is also true and S1 is the cause of S2.
  • D
    S1 is true, S2 is also true but the statements are independant.
✓

Answer

  1. S1 is true, S2 is also true and S1 is the cause of S2.

We know, the electric field intensity E and electric potential V are related $\text{E}=\frac{\text{dV}}{\text{dr}}$.
If electric field intensity  E= 0, then $\frac{\text{dV}}{\text{dr}}=0$.  It means, E = 0 inside the charged conducting sphere causes uniform potential inside the sphere. Hence uniform electrostatic potential 100 V will be at any point inside the sphere.

Important points:

  1. The electric field zero does not necessary imply that electric potential is zero. E.g., the electric field intensity at any point inside the charged spherical shell is zero but there may exist non-zero electric potential.
  2. If two charged particles of same magnitude but opposite sign are placed, the electric potential at the midpoint will be zero but electric field is not equal to zero.

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