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A charged conducting sphere has an electrostatic potential of 100 V on its surface. Consider two statements: S1 - the electric field at every point inside the sphere is zero; S2 - the electrostatic potential at every point inside the sphere is 100 V. Which option correctly describes these statements and their relationship?

1. S1 is true but S2 is false.
2. Both S1 and S2 are false.
3. S1 is true, S2 is also true, and S1 is the cause of S2.
4. S1 is true, S2 is also true but the two statements are independent.

Correct answer: S1 is true, S2 is also true, and S1 is the cause of S2.

Solution

For a charged conductor in electrostatic equilibrium, the field inside is zero (S1 true). Because E = -dV/dr, zero field inside means the potential does not vary, so the interior is at the same potential as the surface, 100 V (S2 true). Thus the zero interior field (S1) is precisely the reason the interior potential is constant and equal to the surface value (S2), so S1 is the cause of S2.

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