The electrostatic potential on the surface of a charged conducting sphere is 100V. Two statements
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 100 V.
Which of the following is a correct statement? [NCERT Exemplar]

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S₁ is true but S₂ is false.

Both S₁ and S₂ are false.

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

S₁ is true, S₂ is also true but the statements are independent.

answer is C.

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Detailed Solution

In this problem, the electric field intensity E and electric potential V are related as $E = - \frac{dV}{dr} .$

Electric field intensity, E = 0 suggest that, $\frac{dV}{dr} = 0$

This imply that V = constant.
Thus, E = 0 inside the charged conducting sphere causes, the same electrostatic potential 100 V at any point inside the sphere.
Note V equals zero does not necessary imply that E = 0 e.g., the electric potential at any point on the perpendicular bisector due to electric dipole is zero but E not.
E = 0 does not necessary imply that V = 0 e.g., the electric field intensity at any point inside the charged spherical shell is zero but there may exist non-zero electric potential.

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