Question

Is electric field intensity scalar or vector?

Answer 1

Electric field intensity is a vector quantity. It has both magnitude and direction, indicating the strength of the electric field and the direction in which a positive test charge would move in that field.

Answer 2

Electric field intensity is a vector quantity.

Here's a detailed explanation:

1. **Definition**: Electric field intensity, often referred to simply as the electric field, represents the force experienced by a positive test charge placed in the field. It is defined as the force per unit positive charge. Mathematically, it is expressed as:
   \[
   \mathbf{E} = \frac{\mathbf{F}}{q}
   \]
   where \( \mathbf{E} \) is the electric field intensity, \( \mathbf{F} \) is the force experienced by the test charge, and \( q \) is the magnitude of the test charge.

2. **Vector Nature**: Because electric field intensity is defined as the force per unit charge, and force is a vector quantity, the electric field must also be a vector. This means it has both magnitude and direction. The direction of the electric field is defined as the direction of the force that a positive test charge would experience. For instance, if you place a positive test charge in the field of another positive charge, the field will point away from the positive source charge. Conversely, if the source charge is negative, the field will point towards it.

3. **Representation**: In vector notation, the electric field intensity at a point in space is represented by a vector \( \mathbf{E} \), which points in the direction that a positive test charge would move if placed at that point. The magnitude of the vector represents the strength of the electric field at that point.

4. **Example**: Consider a positive charge \( Q \) placed at the origin of a coordinate system. The electric field \( \mathbf{E} \) at a point \( \mathbf{r} \) in space, located at distance \( r \) from the charge, is given by:
   \[
   \mathbf{E} = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r^2} \hat{\mathbf{r}}
   \]
   where \( \hat{\mathbf{r}} \) is a unit vector pointing from the charge to the point in question. Here, \( \mathbf{E} \) has both magnitude and direction, indicating that it is a vector quantity.

To summarize, the electric field intensity is a vector because it describes not just the strength of the field but also its direction, which is crucial for understanding how charges interact in the field.