Verified Solution • 2025–26 Session moderate

QPages 165-170: Q43: HC Verma: Concepts of Physics - Volume 2 Capacitors Pages 165-170: Q43 Solution: A large conducting plane has a surface charge density . Find…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the electric field of a conducting plane ($E = \sigma/\epsilon_0$) with that of a non-conducting sheet ($E = \sigma/(2\epsilon_0)$), leading to an error factor of 4 in the energy calculation. Always verify the physical nature of the source to select the correct field expression before substituting into the energy density formula.

A large conducting plane has a surface charge density 1.0×10−4 C m−21.0 \times 10^{-4} \text{ C m}^{-2}. Find the electrostatic energy stored in a cubical volume of edge 1.0 cm in front of the plane.

Step-by-Step Verified Solution

**Answer:** U=5.65×10−5U = 5.65 \times 10^{-5} J. **Step-by-Step Explanation:** σ=1.0×10−4\sigma = 1.0 \times 10^{-4} C/m_. E=σ/ϵ0=1.13×107E = \sigma/\epsilon_0 = 1.13 \times 10^7 N/C. Volume = (0.01)3=10−6(0.01)^3 = 10^{-6} m_.
U=ϵ0E22×V=8.85×10−12×(1.13×107)22×10−6=5.65×10−5 JU = \frac{\epsilon_0 E^2}{2} \times V = \frac{8.85 \times 10^{-12} \times (1.13 \times 10^7)^2}{2} \times 10^{-6} = 5.65 \times 10^{-5} \text{ J}

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