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QPages 141-142: Q12: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q12 Solution: A charge Q is placed at the centre of an uncharged, hollow…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that adding a net charge $q$ to the conductor alters the induced charge on the inner wall, but the inner surface must always carry $-Q$ to cancel the field of the central charge; any extra charge resides on the outer surface, so the cavity field remains $E=kQ/x^{2}$ and is never zero.

A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a. a) Find the surface charge densities on the inner and outer surfaces. b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and outer surfaces? c) Find the electric field inside the sphere at a distance x from the centre in the situations a) and b).

Step-by-Step Verified Solution

**Answer:** (a) Inner: −Q/(4πa2)-Q/(4\pi a^2), Outer: +Q/(4πa2)+Q/(4\pi a^2) (b) Inner: −Q/(4πa2)-Q/(4\pi a^2), Outer: (Q+q)/(4πa2)(Q+q)/(4\pi a^2) (c) E=kQx2E = \frac{kQ}{x^2} for both cases. **Step-by-Step Explanation:** (a) Charge Q at centre induces −Q-Q on inner surface and +Q+Q on outer surface. (b) If charge q is put on the sphere, total charge on outer surface = Q + q. (c) For a point inside the sphere at distance x from centre, the field is due to the central charge Q only (the shell's charges produce zero field inside the cavity by Gauss's law). E=kQx2E = \frac{kQ}{x^2} .

All Questions in this Chapter

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