The application of Gauss's theorem gives rise to an easy evolution of electric field in the case of

Options

A. A charged body of any geometrical configuration
B. A charged body of regular geometrical configuration
C. Revolving charged bodies
D. Charges forming dipoles

Answer

To solve the question regarding the application of Gauss's theorem and its ease of evaluating the electric field for different geometrical configurations, we can follow these steps:

### Step 1: Understand Gauss's Theorem
Gauss's theorem states that the electric flux (Φ) through a closed surface is equal to the charge (Q) enclosed by that surface divided by the permittivity of free space (ε₀):
\[ \Phi = \frac{Q}{\epsilon_0} \]

### Step 2: Relate Electric Field to Flux
The electric flux can also be expressed in terms of the electric field (E) and the surface area (S) of the closed surface:
\[ \Phi = E \cdot S \]
Where \(E\) is the electric field and \(S\) is the surface area through which the field lines pass.

### Step 3: Combine the Two Equations
By combining the two equations from Steps 1 and 2, we can express the electric field as:
\[ E \cdot S = \frac{Q}{\epsilon_0} \]
From this, we can derive the electric field:
\[ E = \frac{Q}{\epsilon_0 \cdot S} \]

### Step 4: Analyze Geometrical Configurations
Now, we need to evaluate the types of geometrical configurations for which we can easily determine the surface area (S):
- For **irregular shapes**: Determining the surface area is complex and often not straightforward.
- For **regular geometrical shapes** (like spheres, cylinders, and cubes): The surface area can be calculated easily using standard formulas.

### Step 5: Conclusion
Since Gauss's theorem allows for straightforward evaluation of the electric field primarily in cases where the surface area can be easily calculated, the best option is:
- **Charged body of regular geometrical configuration** (like spheres, cylinders, or cubes).

Thus, the answer to the question is that the application of Gauss's theorem gives rise to an easy evaluation of electric field in the case of a **charged body of regular geometrical configuration**.

### Final Answer
The correct option is: **Charged body of regular geometrical configuration**.

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