Question

The figure shows four charges fixed on the vertex of a square in the horizontal plane. A charged bead is constrained to move along a wire passing through the centre of the square. Mark the correct statement(s).

• A. In gravity free space, a positively charged bead cannot be in equilibrium at any position.
  
• B. In gravity free space, a negatively charged bead cannot be in equilibrium at any position.
  
• C. In the presence of gravity, a negatively charged bead cannot be in equilibrium position above the plane of fixed charges.
  
• D. In the presence of gravity, a positively charged particle can be in equilibrium above the plane of the fixed charges.
  

Answer 1

Answer: (C), (D)

In the presence of gravity, a positively charged particle can be in equilibrium above the plane of the fixed charges.


When the bead (either positively or negatively charged) is at the centre of the square, the net force will be zero in the absence of gravity. So, it will be in equilibrium.

In the presence of gravity, negatively charged bead above the plane of fixed charges will be attracted downward by fixed charges and gravity. So, it cannot remain in equilibrium.

Also, in the presence of gravity, positively charged bead above the plane of fixed charges can remain in equilibrium because it will be repelled upward by the fixed charges but attracted downward by the gravity.