Assertion (A): Electric potential and electric potential energy are two different quantities.
Reason (R ): For a test charge Q and a point charge Q, the electric potential energy becomes equal to the potential.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is True

Explanation

To solve the assertion and reason question, we need to analyze both the assertion (A) and the reason (R) provided in the question.

### Step 1: Analyze the Assertion (A)
The assertion states that "Electric potential and electric potential energy are two different quantities."

- **Electric Potential (V)**: It is defined as the amount of electric potential energy per unit charge at a point in space. The formula for the electric potential \( V \) due to a point charge \( Q \) at a distance \( r \) is given by:
\[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r} \]
The unit of electric potential is volts (V).

- **Electric Potential Energy (U)**: It is the energy possessed by a charge due to its position in an electric field. For a system of two point charges \( Q \) and \( q \) separated by a distance \( r \), the electric potential energy \( U \) is given by:
\[ U = \frac{1}{4 \pi \epsilon_0} \frac{Qq}{r} \]
The unit of electric potential energy is joules (J).

Since electric potential is measured in volts and electric potential energy is measured in joules, they are indeed two different quantities.

### Conclusion for Assertion (A):
The assertion is **True**.

### Step 2: Analyze the Reason (R)
The reason states that "For a test charge Q and a point charge Q, the electric potential energy becomes equal to the potential."

- The electric potential energy \( U \) for a test charge \( q \) in the field of a point charge \( Q \) at a distance \( r \) is given by:
\[ U = \frac{1}{4 \pi \epsilon_0} \frac{Qq}{r} \]

- The electric potential \( V \) at that point due to the charge \( Q \) is given by:
\[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r} \]

Now, if we consider the electric potential energy in terms of the test charge \( q \):
\[ U = qV \]
This shows that electric potential energy is not equal to electric potential; rather, it is the product of the test charge and the electric potential.

### Conclusion for Reason (R):
The reason is **False**.

### Final Conclusion:
- Assertion (A) is **True**.
- Reason (R) is **False**.

### Answer:
The correct answer is that Assertion (A) is true and Reason (R) is false.

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