Which of the following is not true ?

Options

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

Answer

To solve the question "Which of the following is not true?" regarding electrostatic potential and capacitors, we will analyze the statements related to point charges and dipoles.

### Step-by-Step Solution:

1. **Understanding Electrostatic Potential for a Point Charge:**
- The electrostatic potential \( V \) at a distance \( r \) from a point charge \( q \) is given by the formula:
\[ V = \frac{kq}{r} \]
- Here, \( k \) is Coulomb's constant. This shows that the potential is inversely proportional to \( r \).

2. **Understanding Electric Field for a Point Charge:**
- The electric field \( E \) at a distance \( r \) from a point charge \( q \) is given by:
\[ E = \frac{kq}{r^2} \]
- This indicates that the electric field varies as \( \frac{1}{r^2} \).

3. **Understanding Electrostatic Potential for a Dipole:**
- For an electric dipole consisting of charges \( +q \) and \( -q \) separated by a distance \( 2a \), the potential \( V \) at a point in space at a distance \( r \) (where \( r \) is much larger than \( a \)) can be expressed as:
\[ V = \frac{k \cdot p \cdot \cos \theta}{r^2} \]
- Here, \( p \) is the dipole moment, and \( \theta \) is the angle between the dipole moment vector and the position vector. This shows that the potential varies as \( \frac{1}{r^2} \) at large distances.

4. **Identifying the Incorrect Statement:**
- The statements regarding the electrostatic potential and electric field for point charges and dipoles are:
- For a point charge, potential varies as \( \frac{1}{r} \) (True).
- For a point charge, electric field varies as \( \frac{1}{r^2} \) (True).
- For a dipole, potential depends on the position vector and dipole moment vector (True).
- For a dipole, potential varies as \( \frac{1}{r} \) (False; it varies as \( \frac{1}{r^2} \)).
- Therefore, the statement that "the potential for a dipole varies as \( \frac{1}{r} \)" is not true.

### Conclusion:
The statement that is not true is that the potential for a dipole varies as \( \frac{1}{r} \); it actually varies as \( \frac{1}{r^2} \).