Consider the following statements and choose the correct option.
. I The torque on the dipole is p x E
II The resultant force on the dipole is zero.

Options

A. I and It bath are correct
B. I and II both are incorrect
C. I is correct and II is incorrect
D. I is incorrect and II is correct

Answer

To solve the question regarding the statements about the electric dipole, we will analyze each statement step by step.

### Step 1: Analyze Statement I
**Statement I:** The torque on the dipole is \( \vec{\tau} = \vec{p} \times \vec{E} \).

1. **Understanding Torque on a Dipole:**
- The torque (\( \vec{\tau} \)) experienced by an electric dipole in an electric field (\( \vec{E} \)) is given by the vector cross product of the dipole moment (\( \vec{p} \)) and the electric field (\( \vec{E} \)).
- Mathematically, this is expressed as:
\[ \vec{\tau} = \vec{p} \times \vec{E} \]
- This means that the torque is dependent on both the magnitude and direction of the dipole moment and the electric field.

**Conclusion for Statement I:** This statement is **correct**.

### Step 2: Analyze Statement II
**Statement II:** The resultant force on the dipole is zero.

2. **Understanding the Resultant Force on a Dipole:**
- An electric dipole consists of two equal and opposite charges (+Q and -Q) separated by a distance \( d \).
- When placed in a uniform electric field, the force on the positive charge is \( \vec{F}_{+} = +Q \vec{E} \) and the force on the negative charge is \( \vec{F}_{-} = -Q \vec{E} \).
- The net force (\( \vec{F}_{net} \)) acting on the dipole can be calculated as:
\[ \vec{F}_{net} = \vec{F}_{+} + \vec{F}_{-} = +Q \vec{E} - Q \vec{E} = 0 \]
- This indicates that the forces on the two charges cancel each other out, resulting in no net force acting on the dipole.

**Conclusion for Statement II:** This statement is also **correct**.

### Final Conclusion
Both statements are correct. Therefore, the correct option is:
- **Option A:** Both statements are correct.