The Electric field at a point is

Options

A. always continuous
B. continuous if there is no charge at that point.
C. discontinuous only if there is a negative charge at that point
D. None of these

Explanation

To solve the question regarding the continuity of the electric field at a point, we will analyze the conditions under which the electric field can be continuous or discontinuous based on the presence of charges.

### Step-by-Step Solution:

1. **Understanding Electric Field**:
The electric field (E) at a point in space is defined as the force (F) experienced by a unit positive test charge (q) placed at that point. Mathematically, it is expressed as:
\[ E = \frac{F}{q} \]

2. **Electric Field Due to a Point Charge**:
For a point charge \( Q \), the electric field at a distance \( R \) from the charge is given by:
\[ E = \frac{kQ}{R^2} \]
where \( k \) is Coulomb's constant.

3. **Case of No Charge at the Point**:
If there are no charges present at the point where we are measuring the electric field, the electric field lines will be continuous. This is because the electric field produced by the source charge \( Q \) will not be interrupted by any other charge.

4. **Case of Charges Present**:
If there is a charge present at the point (either positive or negative), the electric field can become discontinuous. For example:
- If a positive charge \( +Q \) is surrounded by a negative charge \( -Q \), the electric field lines will start from the positive charge and end at the negative charge. Inside the region of the negative charge, the electric field is zero, leading to a discontinuity.
- Similarly, if there are two positive charges nearby, the electric field lines may cancel out in certain regions, leading to points where the electric field is zero, thus creating discontinuities.

5. **Conclusion on Continuity**:
Based on the analysis:
- The electric field is continuous if there are no charges present at the point.
- The electric field is discontinuous if there is any charge present in the vicinity, whether it is positive or negative.

6. **Final Answer**:
Therefore, the correct answer to the question is that the electric field at a point is continuous only if there is no charge at that point. If there is any charge present, the electric field will be discontinuous.