Question

Consider two identical charges placed at a distance 2d apart as shown in the figure. The equilibrium of a positive test charge placed at point 0 midway between them may be:

• A. Neutral
• B. Stable for displacement along the X-axis
• C. Stable for displacement along the y-axis
• D. Unstable for displacement along the x-axis

Answer 1

Answer: (B), (C), (D)

The correct options are
B Stable for displacement along the X-axis
C Stable for displacement along the y-axis
D Unstable for displacement along the x-axis

let the two charges be negative then,
when the test charge is displaced along y axis both the charges will apply a attractive force towards the origin, hence it is stable equilibrium.
when displaced along x axis the force by the charge nearer to the test charge will increase while force due to the other charge will decrease forcing the test charge to move away from the equilibrium point , hence it is a unstable equilibrium.
second case will be when the two charges is also positive,
when the test charge is displaced along y direction the repulsive force acting on it , will throw it more and more away
when displaced along x axis the force of repulsion due to nearer one will be more than the farther one , hence the test charge will return to equilibrium position hence stable equilibrium.