The SI unit of surface integral of electric field is:

Options

A. V
B. N/C
C. Vm
D. `C//m^2`

Explanation

To find the SI unit of the surface integral of the electric field, we can follow these steps:

### Step 1: Understand the concept of surface integral of electric field
The surface integral of the electric field is related to the electric flux through a surface. According to Gauss's law, the electric flux (Φ) through a surface is given by the integral of the electric field (E) over that surface area (A):
\[ \Phi = \iint_S \mathbf{E} \cdot d\mathbf{S} \]
where \(d\mathbf{S}\) is a differential area vector on the surface.

### Step 2: Identify the units of electric field and area
The electric field (E) has the SI unit of volts per meter (V/m). The area (A) has the SI unit of square meters (m²).

### Step 3: Calculate the unit of the surface integral
To find the unit of the surface integral of the electric field, we multiply the unit of the electric field by the unit of area:
\[ \text{Unit of } \Phi = \text{Unit of } E \times \text{Unit of } A = \left(\frac{\text{V}}{\text{m}}\right) \times \text{m}^2 \]

### Step 4: Simplify the expression
Now, we simplify the expression:
\[ \text{Unit of } \Phi = \frac{\text{V}}{\text{m}} \times \text{m}^2 = \text{V} \cdot \text{m} \]

### Conclusion
Thus, the SI unit of the surface integral of the electric field is:
\[ \text{V} \cdot \text{m} \quad (\text{volts times meters}) \]

### Final Answer
The correct option is **volt meter (V·m)**.

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