The unit of physical quantity obtained by the line integral of electric field is

Options

A. `NC^(-1)`
B. `Vm^(-1)`
C. `JC^(-1)`
D. `C^(2)N^(-1) m^(-2)`

Answer

To solve the question regarding the unit of the physical quantity obtained by the line integral of electric field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Line Integral of Electric Field**:
The line integral of the electric field \( \mathbf{E} \) along a path is represented mathematically as:
\[ V = -\int \mathbf{E} \cdot d\mathbf{l} \]
where \( V \) is the electric potential difference between two points.

2. **Relating Electric Field to Potential**:
The electric field \( \mathbf{E} \) is related to the electric potential \( V \) by the equation:
\[ \mathbf{E} = -\frac{dV}{dl} \]
This implies that the electric field is the negative gradient of the electric potential.

3. **Line Integral Interpretation**:
When we perform the line integral of the electric field, we are essentially calculating the potential difference:
\[ \int \mathbf{E} \cdot d\mathbf{l} = V \]
Thus, the line integral of the electric field gives us the electric potential difference \( V \).

4. **Units of Electric Potential**:
The unit of electric potential \( V \) is defined as:
\[ V = \frac{W}{Q} \]
where \( W \) is the work done (in Joules) and \( Q \) is the charge (in Coulombs). Therefore, the unit of electric potential is:
\[ \text{Volt} = \frac{\text{Joule}}{\text{Coulomb}} = \text{J/C} \]

5. **Conclusion**:
Since the line integral of the electric field results in the electric potential, the unit of the physical quantity obtained by this line integral is:
\[ \text{Volt} \quad \text{(or Joule per Coulomb)} \]

### Final Answer:
The unit of the physical quantity obtained by the line integral of electric field is **Volt** (or Joule per Coulomb).