In case of large or curved surface, flux can be found by

Options

A. Integrating product `E.triangleS`all over the surface
B. Integrating product `ExxtriangleS` all over the surface
C. by treating surface as plane surface and then flux `phi=E.A`
D. by using Coulomb’s law

Answer

To find the electric flux through a large or curved surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Flux**:
Electric flux (Φ) through a surface is defined as the number of electric field lines passing through that surface. It is mathematically represented as:
\[ \Phi = \int \mathbf{E} \cdot d\mathbf{S} \]
where \( \mathbf{E} \) is the electric field vector and \( d\mathbf{S} \) is the differential area vector on the surface.

2. **Choosing a Small Element**:
For a large or curved surface, it is impractical to calculate the flux directly over the entire surface. Instead, we consider a small differential area \( dS \) on the surface.

3. **Calculating the Dot Product**:
For each small area element, we calculate the dot product \( \mathbf{E} \cdot d\mathbf{S} \). This gives us the contribution to the electric flux from that small area.

4. **Integrating Over the Surface**:
To find the total flux through the entire surface, we integrate the dot product over the entire surface area \( S \):
\[ \Phi = \int_S \mathbf{E} \cdot d\mathbf{S} \]
This integral sums up the contributions from all the small area elements across the surface.

5. **Final Result**:
The final expression for the electric flux through a large or curved surface is given by the integral:
\[ \Phi = \int \mathbf{E} \cdot d\mathbf{S} \]
This method is applicable for any surface, regardless of its shape, as long as the electric field is known.