Verified Solution • 2025–26 Session moderate

QPages 165-170: Q41: HC Verma: Concepts of Physics - Volume 2 Capacitors Pages 165-170: Q41 Solution: A point charge Q is placed at the origin. Find the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently integrate the field‑energy density from $r=0$ to $\infty$, forgetting the problem asks only for the region outside a sphere of radius $R$; this yields the divergent self‑energy of a point charge. Start the integral at $R$ and retain the $\tfrac12\epsilon_0E^2$ factor to obtain $U=\frac{Q^2}{8\pi\epsilon_0 R}\,$.

A point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.

Step-by-Step Verified Solution

**Answer:**

U = \frac{Q^2}{8\pi\epsilon_0 R}

. **Step-by-Step Explanation:** Energy stored outside sphere of radius R:

U = \int_R^\infty \frac{\epsilon_0 E^2}{2} 4\pi r^2 dr = \frac{Q^2}{8\pi\epsilon_0 R}

All Questions in this Chapter

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