Consider the following statements about electric dipole and select the correct ones.
`S_(1)`: Electric dipole moment vector `vec(p)` is directed from the negative charge to the positive charge
`S_(2)`: The electric field of a dipole potential falls off as `(1)/(r^(2))` and not as `(1)/(r )`
`S_(3)`: The electric field of a dipole at a point with position vector `vec(r )` depends on `|vec(r )|` as well as s angle between `vec(r ) and vec(p)`
`S_(4)`: In a uniform electric field, the electric dipole experience no net force but a torque

Options

A. `S_(2), S_(3) and S_(4)`
B. `S_(2) and S_(4)`
C. `S_(2) and S_(3)`
D. all four

Answer

To solve the question regarding the statements about electric dipoles, we will analyze each statement one by one and determine whether they are correct or incorrect.

### Step 1: Analyze Statement S1
**Statement S1**: Electric dipole moment vector \( \vec{p} \) is directed from the negative charge to the positive charge.

**Analysis**: This statement is correct. By definition, the electric dipole moment \( \vec{p} \) is defined as the vector pointing from the negative charge to the positive charge. Therefore, this statement is true.

### Step 2: Analyze Statement S2
**Statement S2**: The electric field of a dipole potential falls off as \( \frac{1}{r^2} \) and not as \( \frac{1}{r} \).

**Analysis**: This statement is incorrect. The electric field \( E \) due to a dipole at a point in space falls off as \( \frac{1}{r^3} \) in the far field region, not \( \frac{1}{r^2} \). The potential \( V \) due to a dipole falls off as \( \frac{1}{r^2} \), but the electric field itself behaves differently. Thus, this statement is false.

### Step 3: Analyze Statement S3
**Statement S3**: The electric field of a dipole at a point with position vector \( \vec{r} \) depends on \( |\vec{r}| \) as well as the angle between \( \vec{r} \) and \( \vec{p} \).

**Analysis**: This statement is correct. The electric field \( E \) due to a dipole does depend on both the distance \( |\vec{r}| \) from the dipole and the angle \( \theta \) between the dipole moment \( \vec{p} \) and the position vector \( \vec{r} \). Therefore, this statement is true.

### Step 4: Analyze Statement S4
**Statement S4**: In a uniform electric field, the electric dipole experiences no net force but a torque.

**Analysis**: This statement is correct. In a uniform electric field, the forces on the two charges of the dipole are equal in magnitude and opposite in direction, resulting in a net force of zero. However, the dipole will experience a torque that tends to align it with the electric field. Thus, this statement is true.

### Conclusion
After analyzing all statements, we find:
- **S1**: Correct
- **S2**: Incorrect
- **S3**: Correct
- **S4**: Correct

The correct statements are S1, S3, and S4.

### Final Answer
The correct options are S1, S3, and S4.

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