The Gaussian surface for calculating the electric field due to a charge distribution is

Options

A. (a)any surface near the charge distribution
B. (b) always a spherical surface
C. (c) a symmetrical closed surface containing the charge distribution, at very point of which electric field has a single fixed value
D. (d) None of the given options

Answer

To solve the question regarding the Gaussian surface for calculating the electric field due to a charge distribution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Gauss's Law**:
Gauss's Law states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space (ε₀). Mathematically, it is expressed as:
\[ \Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0} \]
where \( \Phi_E \) is the electric flux, \( \vec{E} \) is the electric field, \( d\vec{A} \) is the differential area vector, and \( Q_{enc} \) is the enclosed charge.

2. **Choosing a Gaussian Surface**:
The Gaussian surface should be chosen based on the symmetry of the charge distribution. Common symmetrical shapes include:
- Spherical surfaces for point charges or uniformly charged spheres.
- Cylindrical surfaces for infinitely long charged wires.
- Planar surfaces for infinite charged planes.

3. **Symmetry Consideration**:
The key to applying Gauss's Law effectively is to ensure that the electric field has the same magnitude and direction at every point on the Gaussian surface. This is typically achieved when the surface is symmetrical with respect to the charge distribution.

4. **Electric Field Calculation**:
Once the appropriate Gaussian surface is selected, you can calculate the electric field by evaluating the surface integral of the electric field over the Gaussian surface. If the electric field is constant over the surface, the integral simplifies to:
\[ \Phi_E = E \cdot A \]
where \( A \) is the area of the Gaussian surface.

5. **Conclusion**:
Therefore, the Gaussian surface for calculating the electric field due to a charge distribution is a symmetrical closed surface that contains the charge distribution. The electric field at every point on this surface should ideally have a single fixed value.

### Final Answer:
The Gaussian surface for calculating the electric field due to a charge distribution is a symmetrical closed surface containing the charge distribution, at every point of which the electric field has a single fixed value.

---