Match the following
`{:(,"Column I",,"Column II"),((A),E prop (1)/(r^(2)),(p),"Point charge"),((B),E prop r,(q),"Spherically symmetric charge distribution"),((C ),V prop (1)/(r ),(r ),"Long line charge"),((D),V_(2)-V_(1)=f((r_(2))/(r_(1))),(s),"Plane sheet of charge"),((E ),V_(2)-V_(1) prop r_(2)-r_(1),(t ),"Electric dipole"):}`

Answer

To solve the matching question, we need to analyze the properties of electric fields and potentials for different charge distributions. Let's break down the information step by step.

### Step 1: Analyze Point Charge
- For a point charge \( q \):
- Electric field \( E \) is given by \( E \propto \frac{1}{r^2} \) (where \( r \) is the distance from the charge).
- Electric potential \( V \) is given by \( V \propto \frac{1}{r} \).

**Matching:**
- This corresponds to option **(p)**.

### Step 2: Analyze Spherically Symmetric Charge Distribution
- For a spherically symmetric charge distribution:
- Electric field outside the sphere \( E \) is \( E \propto \frac{1}{r^2} \).
- Electric field inside the sphere \( E \) is \( E \propto r \).
- Electric potential outside the sphere \( V \) is \( V \propto \frac{1}{r} \).

**Matching:**
- This corresponds to option **(q)**.

### Step 3: Analyze Long Line Charge
- For a long line charge:
- Electric field \( E \) is given by \( E \propto \frac{1}{r} \).
- The potential difference \( V_2 - V_1 \) can be expressed as \( V_2 - V_1 \propto \ln\left(\frac{r_2}{r_1}\right) \).

**Matching:**
- This corresponds to option **(r)**.

### Step 4: Analyze Plane Sheet of Charge
- For a plane sheet of charge:
- Electric field \( E \) is constant and does not depend on \( r \).
- The potential difference \( V_2 - V_1 \) is proportional to \( r_2 - r_1 \).

**Matching:**
- This corresponds to option **(s)**.

### Step 5: Analyze Electric Dipole
- For an electric dipole:
- Electric field \( E \) is given by \( E \propto \frac{1}{r^3} \).
- The potential difference \( V_2 - V_1 \) is proportional to \( \frac{1}{r_2^2} - \frac{1}{r_1^2} \).

**Matching:**
- This corresponds to option **(t)**.

### Final Matching Summary:
- **A** matches with **(p)** (Point charge).
- **B** matches with **(q)** (Spherically symmetric charge distribution).
- **C** matches with **(r)** (Long line charge).
- **D** matches with **(s)** (Plane sheet of charge).
- **E** matches with **(t)** (Electric dipole).

### Final Answer:
- A - p
- B - q
- C - r
- D - s
- E - t