Column I shows charge distribution and column II shows electrostatic field created by that charge at a point r distance from its centre.
`{:(,"Column I ",,"Column II"),((A),"A stationary point charge",(p),E prop r^(0)),((B),"A stationary uniformly long charge rod",(q),Eprop r^(1)),((C ), "A stationary electric dipole",(r ),E prop r^(*-1)),,(s),E prop r^(-2) ),(,,(t ),E propr^(-3)):} `

Answer

To solve the question regarding the electrostatic field created by different charge distributions at a distance \( r \) from their center, we will analyze each case step by step.

### Step 1: Analyze the stationary point charge
For a stationary point charge \( Q \), the electric field \( E \) at a distance \( r \) from the charge is given by the formula:
\[ E = \frac{kQ}{r^2} \]
This indicates that the electric field is inversely proportional to the square of the distance \( r \):
\[ E \propto \frac{1}{r^2} \]
Thus, the correct match from Column II for a stationary point charge (A) is:
- \( E \propto r^{-2} \) (which corresponds to option S).

### Step 2: Analyze the stationary uniformly long charge rod
For a long uniformly charged rod with linear charge density \( \lambda \), the electric field \( E \) at a distance \( r \) from the rod is given by:
\[ E = \frac{2k\lambda}{r} \]
This shows that the electric field is inversely proportional to the distance \( r \):
\[ E \propto \frac{1}{r} \]
Thus, the correct match from Column II for a stationary uniformly long charge rod (B) is:
- \( E \propto r^{-1} \) (which corresponds to option Q).

### Step 3: Analyze the stationary electric dipole
For a stationary electric dipole consisting of two equal and opposite charges separated by a distance \( d \), the electric field \( E \) at a point along the axis of the dipole at a distance \( r \) (where \( r \) is much larger than \( d \)) is given by:
\[ E = \frac{2kp}{r^3} \]
where \( p \) is the dipole moment. This indicates that the electric field is inversely proportional to the cube of the distance \( r \):
\[ E \propto \frac{1}{r^3} \]
Thus, the correct match from Column II for a stationary electric dipole (C) is:
- \( E \propto r^{-3} \) (which corresponds to option T).

### Summary of Matches
- A (Stationary point charge) matches with S: \( E \propto r^{-2} \)
- B (Stationary uniformly long charge rod) matches with Q: \( E \propto r^{-1} \)
- C (Stationary electric dipole) matches with T: \( E \propto r^{-3} \)

### Final Answer
- A → S
- B → Q
- C → T