Choose the correct statements :-
(a) The density of electric lines of force at a point is independent of the magnitude of electric intensity vector E at that point
(b) The density of electric lines of force at a point is proportional to the magnitude of electric intensity vector E at that point
(c ) Actually, the electric field lines do not exist. This is just a graphical description of the electric field
(d) Actually, the electric field lines exist

Options

A. b, c
B. c, d
C. b, d
D. a, d

Answer

To solve the question, let's analyze each statement one by one:

### Step 1: Analyze Statement (a)
**Statement (a):** The density of electric lines of force at a point is independent of the magnitude of electric intensity vector E at that point.

- **Explanation:** The density of electric field lines is directly related to the strength of the electric field. If the electric field is strong, the lines are closer together, indicating a higher density of lines. Therefore, this statement is **incorrect**.

### Step 2: Analyze Statement (b)
**Statement (b):** The density of electric lines of force at a point is proportional to the magnitude of electric intensity vector E at that point.

- **Explanation:** As mentioned earlier, the density of electric field lines is indeed proportional to the magnitude of the electric field intensity. The closer the lines are, the stronger the electric field. Hence, this statement is **correct**.

### Step 3: Analyze Statement (c)
**Statement (c):** Actually, the electric field lines do not exist. This is just a graphical description of the electric field.

- **Explanation:** Electric field lines are a conceptual tool used to represent the electric field visually. They do not physically exist in space; they are a way to illustrate the direction and strength of the field. Therefore, this statement is **correct**.

### Step 4: Analyze Statement (d)
**Statement (d):** Actually, the electric field lines exist.

- **Explanation:** This statement contradicts the previous analysis. Electric field lines are not physical entities; they are a representation of the electric field. Thus, this statement is **incorrect**.

### Final Conclusion:
- The correct statements are **(b)** and **(c)**.