A test charge is moved from lower potential point to a higher potential point. The potential energy of test charge will :

Options

A. remains the same
B. increase
C. decrease
D. becomes zero

Answer

To solve the question regarding the potential energy of a test charge moved from a lower potential point to a higher potential point, we can follow these steps:

### Step 1: Understand the Concept of Electric Potential
Electric potential (V) at a point in an electric field is defined as the amount of work done in bringing a unit positive charge from infinity to that point without any acceleration. Higher potential means more work is required to bring a charge to that point.

**Hint:** Recall that electric potential is a measure of potential energy per unit charge.

### Step 2: Identify the Direction of Electric Field
In a uniform electric field, the electric field (E) points from higher potential to lower potential. Therefore, when a test charge is moved from a lower potential (point B) to a higher potential (point A), it is moving against the direction of the electric field.

**Hint:** Remember that the electric field direction indicates where the potential decreases.

### Step 3: Analyze the Movement of the Test Charge
When the test charge (let's say +Q) is moved from point B (lower potential) to point A (higher potential), it is moving against the electric field. This means that work is done on the charge to move it to a higher potential.

**Hint:** Think about the work-energy principle: work done on the charge results in an increase in its energy.

### Step 4: Relate Potential and Potential Energy
The potential energy (U) of a charge in an electric field is given by the formula:
\[ U = Q \cdot V \]
where \( Q \) is the charge and \( V \) is the electric potential at that point. Since the charge is moving to a higher potential, the value of V increases.

**Hint:** Remember that potential energy is directly proportional to both the charge and the electric potential.

### Step 5: Conclusion on Potential Energy Change
As the test charge moves from a lower potential to a higher potential, both the potential (V) and the potential energy (U) of the test charge increase. Therefore, the potential energy of the test charge will increase.

**Final Answer:** The potential energy of the test charge will **increase**.