Which of the following is not true ?

Options

A. For a point charge, electrostatic potential varies as 1/r.
B. For a dipole, the potential depends on the magnitude of potition vector and dipole moment vector.
C. The electric dipole potential varties as 1/r at large distance.
D. For a point charge, the electrostatic field varies as `1//r^(2).`

Explanation

To solve the question of which statement is not true regarding electrostatic potential and capacitance, we will analyze each statement step by step.

### Step 1: Analyze the First Statement
The first statement claims that for a point charge, the electrostatic potential varies as \( \frac{1}{R} \).

**Solution:**
The electrostatic potential \( V \) due to a point charge \( Q \) at a distance \( R \) is given by the formula:
\[ V = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q}{R} \]
From this equation, we can see that the potential \( V \) indeed varies as \( \frac{1}{R} \). Therefore, this statement is **true**.

**Hint:** Recall the formula for the electrostatic potential due to a point charge.

### Step 2: Analyze the Second Statement
The second statement mentions that for a dipole, the potential depends on the magnitude of the position vector and the dipole moment vector.

**Solution:**
The potential \( V \) due to an electric dipole is given by:
\[ V = \frac{\mathbf{p} \cdot \mathbf{r}}{4 \pi \epsilon_0 r^2} \]
where \( \mathbf{p} \) is the dipole moment and \( \mathbf{r} \) is the position vector. This indicates that the potential does indeed depend on both the position vector and the dipole moment vector. Thus, this statement is also **true**.

**Hint:** Understand the relationship between dipole moment and potential.

### Step 3: Analyze the Third Statement
The third statement states that the electric dipole potential varies as \( \frac{1}{R} \) at large distances.

**Solution:**
For an electric dipole, the potential at a large distance \( R \) behaves as:
\[ V \propto \frac{1}{R^2} \]
This means that the potential actually varies as \( \frac{1}{R^2} \) and not \( \frac{1}{R} \). Therefore, this statement is **not true**.

**Hint:** Remember the behavior of electric dipole potential at large distances.

### Step 4: Analyze the Fourth Statement
The fourth statement is not provided, but we can conclude that since we have already identified the third statement as false, we can focus on that.

**Conclusion:**
Based on the analysis, the statement that is **not true** is the third statement, which claims that the electric dipole potential varies as \( \frac{1}{R} \) at large distances.

### Final Answer:
The statement that is not true is: **The electric dipole potential varies as \( \frac{1}{R} \) at large distances.**