Which of the following statements about dipole moment is not true?

Options

A. The dimensions of dipole moment is [L T A].
B. The unit of dipole moment is C m.
C. Dipole moment is vector quantity and directed from negative to positive charge.
D. Dipole moment is a scalar quantity and has magnitude charge equal to the potential of separation between charge.

Explanation

To determine which statement about dipole moment is not true, we will evaluate each of the given statements one by one.

### Step 1: Analyze the first statement
**Statement 1:** The dimension of dipole moment is \(L^1 T^1 A^1\).

- The dipole moment (\(P\)) is defined as the product of charge (\(Q\)) and the distance (\(d\)) between the charges.
- The dimensional formula for charge is \([Q] = [I][T] = A^1 T^1\) (where \(I\) is current and \(T\) is time).
- The dimensional formula for distance is \([d] = L^1\).
- Therefore, the dimensional formula for dipole moment is:
\[ [P] = [Q][d] = (A^1 T^1)(L^1) = L^1 A^1 T^1 \]
- This statement is **true**.

### Step 2: Analyze the second statement
**Statement 2:** The unit of dipole moment is coulomb meter.

- The unit of dipole moment is indeed derived from the product of charge and distance.
- Charge is measured in coulombs (C) and distance in meters (m).
- Thus, the unit of dipole moment is:
\[ \text{Unit of } P = \text{C} \cdot \text{m} = \text{coulomb meter} \]
- This statement is **true**.

### Step 3: Analyze the third statement
**Statement 3:** Dipole moment is a vector quantity and it is directed from negative to positive charge.

- By definition, the dipole moment is a vector quantity.
- It is directed from the negative charge to the positive charge, which is consistent with the definition of electric dipoles.
- Therefore, this statement is also **true**.

### Step 4: Analyze the fourth statement
**Statement 4:** Dipole moment is a scalar quantity and has a magnitude equal to the product of charge and separation between the charges.

- This statement incorrectly describes the dipole moment as a scalar quantity.
- The dipole moment is a vector quantity, as established in the previous analysis.
- The magnitude of the dipole moment is indeed given by \(P = Q \cdot d\), but it is not a scalar; it has direction.
- Therefore, this statement is **not true**.

### Conclusion
The statement that is not true about dipole moment is **Statement 4**.

---