The Electric field at a point is
A. always continuous
B. continuous if ther is no charge at that point.
C. discontinuous only if there is a negative charge at that point.
D. discontinuous if there is a charge at that point.

Options

A. A,C are true
B. All are true
C. B,D are true
D. B,C are true

Explanation

To solve the question about the continuity of the electric field at a point, let's analyze the options step by step.

### Step 1: Understanding Electric Field Continuity
The electric field at a point is defined by the behavior of electric field lines. These lines represent the direction and strength of the electric field. A key property of electric field lines is that they cannot cross each other; at any given point in space, the electric field can only have one direction and one magnitude.

### Step 2: Analyzing the Options
- **Option A: Always continuous**
- This option suggests that the electric field is always continuous at any point. However, this is not true because the presence of a charge can cause discontinuities in the electric field. Therefore, this option is incorrect.

- **Option B: Continuous if there is no charge at that point**
- This option states that the electric field is continuous if there is no charge at that point. This is true because if there are no charges present, the electric field lines can extend freely without interruption. Thus, this option is correct.

- **Option C: Discontinuous only if there is a negative charge at that point**
- This option implies that the electric field is discontinuous only when a negative charge is present. However, the presence of any charge (positive or negative) can cause the electric field to be discontinuous. Therefore, this option is incorrect.

- **Option D: Discontinuous if there is a charge at that point**
- This option states that the electric field is discontinuous if there is any charge at that point. This is true because the presence of a charge (whether positive or negative) can cause the electric field lines to terminate or change direction, leading to discontinuity. Thus, this option is correct.

### Step 3: Conclusion
Based on the analysis, the correct answers are **Option B** and **Option D**. The electric field is continuous if there is no charge at that point and discontinuous if there is any charge at that point.

### Final Answer
The correct options are **B** and **D**.

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