The potential gradient is a

Options

A. Vector quantiy
B. Scalar quantity
C. Conversion factor
D. Constant

Answer

To solve the question regarding the nature of the potential gradient, we will analyze the concept step by step.

### Step-by-Step Solution:

1. **Understanding Potential Gradient**:
The potential gradient refers to the rate of change of electric potential (V) with respect to distance in a given direction. It indicates how much the electric potential changes as you move through space.

2. **Mathematical Representation**:
The potential gradient can be mathematically expressed as:
\[ \vec{E} = -\nabla V \]
where \(\nabla V\) (del V) represents the gradient of the potential V, and \(\vec{E}\) is the electric field vector.

3. **Components of the Gradient**:
The gradient can be broken down into its components in three-dimensional space:
\[ \nabla V = \left( \frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k} \right) \]
Here, \(\hat{i}\), \(\hat{j}\), and \(\hat{k}\) are unit vectors in the x, y, and z directions, respectively.

4. **Nature of the Quantity**:
Since the potential gradient has both magnitude and direction (as indicated by the presence of unit vectors), it is classified as a vector quantity.

5. **Conclusion**:
Based on the analysis, we conclude that the potential gradient is indeed a vector quantity.

### Final Answer:
The potential gradient is a **Vector Quantity**.

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