Two positive point charges of unequal magnitude are placed at a certain distance apart. A small positive test charge is placed at null point, then

Options

A. The test charge is in unstable equilibrium
B. The test charge is in stable equilibrium
C. The test charge is in neutral equilibrium
D. The test charge is not in equilibrium

Answer

To solve the problem, we need to analyze the situation of two positive point charges and the behavior of a small positive test charge placed at the null point. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Concept of Null Point
A null point is a location in the electric field where the net electric field due to multiple charges is zero. In this case, we have two positive point charges, \( q_1 \) and \( q_2 \), of unequal magnitudes, separated by a certain distance.

**Hint:** Remember that the electric field due to a positive charge points away from the charge.

### Step 2: Determine the Position of the Null Point
Since the charges are of unequal magnitudes, the null point will not be exactly in the middle between the two charges. It will be closer to the charge with the smaller magnitude.

**Hint:** The position of the null point can be found by setting the electric fields due to both charges equal to each other.

### Step 3: Analyze the Stability of the Test Charge
When a small positive test charge is placed at the null point, it experiences forces due to both \( q_1 \) and \( q_2 \). If the test charge is displaced slightly from the null point, the forces acting on it will not restore it back to the null point.

**Hint:** Consider what happens when you displace the test charge slightly. Does it experience a force that pushes it back to the null point or away from it?

### Step 4: Determine the Nature of Equilibrium
Since the test charge is repelled by both positive charges, if it moves away from the null point, it will continue to move further away due to the repulsive forces. This indicates that the test charge is in unstable equilibrium.

**Hint:** In stable equilibrium, a displaced charge returns to its original position, while in unstable equilibrium, it moves further away.

### Step 5: Conclusion
Based on the analysis, the correct option is that the test charge is in unstable equilibrium.

**Final Answer:** The test charge is in unstable equilibrium.