Three point charges are placed at the corner of an equilateral triangle. Assuming only electrostatic forces are acting.

Options

A. the system can never be in equilibrium
B. the system will be equilibrium if the charges rotate about the centre of the triangle
C. the system will be in equilibrium if the charges have different magnitudes and different signs
D. the system will be in equilibrium if the charges have the same magnitude but different signs.

Explanation

To solve the problem of determining the conditions under which three point charges placed at the corners of an equilateral triangle can be in equilibrium, we can follow these steps:

### Step 1: Understand the Forces Acting on Each Charge
In an equilateral triangle, each charge will experience forces due to the other two charges. If we label the charges as \( q_1 \), \( q_2 \), and \( q_3 \), we need to analyze the forces acting on each charge.

### Step 2: Analyze the Forces on One Charge
Let's consider the charge \( q_1 \). The forces acting on \( q_1 \) due to \( q_2 \) and \( q_3 \) will depend on the nature of the charges (whether they are like or unlike).

- If \( q_2 \) and \( q_3 \) are of the same sign as \( q_1 \), then \( q_1 \) will experience repulsive forces from both \( q_2 \) and \( q_3 \).
- If \( q_2 \) and \( q_3 \) are of opposite sign to \( q_1 \), then \( q_1 \) will experience attractive forces from both.

### Step 3: Conditions for Equilibrium
For \( q_1 \) to be in equilibrium, the net force acting on it must be zero. This can happen if:
1. The magnitudes of the forces acting on \( q_1 \) from \( q_2 \) and \( q_3 \) are equal.
2. The directions of these forces must be opposite.

### Step 4: Analyze the Geometry
In an equilateral triangle, the angles between the lines connecting the charges are \( 60^\circ \). Therefore, the forces due to \( q_2 \) and \( q_3 \) acting on \( q_1 \) cannot be directly opposite to each other. This means that even if the magnitudes of the forces are equal, they cannot cancel each other out due to their directions.

### Step 5: Conclusion
Since the forces cannot be equal and opposite due to the geometry of the triangle, we conclude that it is impossible for the system to be in equilibrium under the influence of electrostatic forces alone.

### Final Answer
The system of three point charges placed at the corners of an equilateral triangle can never be in equilibrium.

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