Question

Electric field at point P is given by $\vec{E} = E_0 \hat{r}$. The total flux through the given cylinder of radius R height h is:

• A. $E_0 \pi R^2h$
• B. $2E_0 \pi R^2h$
• C. $3E_0 \pi R^2h$
• D. $4E_0 \pi R^2h$

Answer 1

The provided solution indicates that none of the options match the calculated flux. Therefore, a correct answer cannot be selected from the given options.

Answer 2

The problem states that the electric field is $\vec{E} = E_0 \hat{r}$. If we interpret $\hat{r}$ as a constant radial direction from the center of the cylinder, and $E_0$ as a constant magnitude, the flux through the curved surface of the cylinder is $\Phi_{side} = \int \vec{E} \cdot d\vec{A} = \int E_0 dA = E_0 (2\pi Rh)$.

However, the provided options are proportional to the volume of the cylinder ($\pi R^2 h$), which suggests a different interpretation or a potential error in the problem statement or options. If the electric field were uniform and directed along the axis of the cylinder, say $\vec{E} = E_0 \hat{k}$, the net flux through the closed cylinder would be zero.

Given the discrepancy and the detailed calculation in the provided raw solution leading to a result not matching any option, it's concluded that there might be an issue with the question or its options. The detailed calculation in the raw solution for a radial electric field is complex and does not yield any of the provided answers. Without further clarification or correction, it's impossible to definitively select a correct answer from the given choices.