Verified Solution • 2025–26 Session moderate

QPages 141-142: Q16: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q16 Solution: A long cylindrical volume contains a uniformly distributed…

A long cylindrical volume contains a uniformly distributed charge of density

\rho

. Find the electric field at a point P inside the cylindrical volume at a distance x from its axis see the figure).

Step-by-Step Verified Solution

**Answer:**

E = \frac{\rho x}{2\epsilon_0}

. **Step-by-Step Explanation:** For a point inside a uniformly charged cylinder at distance x from the axis: Charge enclosed in a coaxial cylinder of radius x and length L:

Q_{enc} = \rho \pi x^2 L

. By Gauss's law:

E \times 2\pi x L = \frac{\rho \pi x^2 L}{\epsilon_0}

.

E = \frac{\rho x}{2\epsilon_0}

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