Units of electric flux are

Options

A. `("N-m"^(2))/(C)`
B. `(N)/(C-m^(2))`
C. Volt-m
D. `"Volt-m"^(3)`

Answer

To determine the units of electric flux, we can start from the definition of electric flux and the relationship between electric field and area.

### Step-by-Step Solution:

1. **Definition of Electric Flux**:
Electric flux (Φ) is defined as the product of the electric field (E) and the area (A) through which the field lines pass. Mathematically, it is expressed as:
\[ Φ = E \cdot A \]

2. **Units of Electric Field**:
The electric field (E) can be defined in terms of force (F) and charge (q):
\[ E = \frac{F}{q} \]
The SI unit of force (F) is Newton (N), and the SI unit of charge (q) is Coulomb (C). Therefore, the units of electric field (E) are:
\[ [E] = \frac{N}{C} \]

3. **Units of Area**:
The SI unit of area (A) is square meter (m²).

4. **Combining Units for Electric Flux**:
Now, substituting the units of electric field and area into the equation for electric flux:
\[ [Φ] = [E] \cdot [A] = \left(\frac{N}{C}\right) \cdot (m^2) = \frac{N \cdot m^2}{C} \]

5. **Alternative Expression for Electric Field**:
Electric field can also be expressed in terms of electric potential (V) and distance (L):
\[ E = \frac{V}{L} \]
Here, V is measured in volts (V) and L in meters (m). Thus, substituting this into the electric flux formula gives:
\[ Φ = E \cdot A = \left(\frac{V}{L}\right) \cdot A \]
The units of electric potential (V) are volts (V), and the area (A) is in square meters (m²). Therefore, we can express the units of electric flux as:
\[ [Φ] = \left(\frac{V}{m}\right) \cdot (m^2) = V \cdot m \]

6. **Final Units of Electric Flux**:
From the two approaches, we find that the units of electric flux can be expressed as:
\[ [Φ] = \frac{N \cdot m^2}{C} \quad \text{or} \quad [Φ] = V \cdot m \]

### Conclusion:
The units of electric flux are \( \frac{N \cdot m^2}{C} \) and \( V \cdot m \).