Four identical positive charges Q are fixed at the vertices of a square. A free charge q is placed at the centre. It is displaced by a very small distance along either diagonal of the square. Which statements are correct?
Select all that apply

Question

Four identical positive charges Q are fixed at the vertices of a square. A free charge q is placed at the centre. It is displaced by a very small distance along either diagonal of the square. Which statements are correct?

Select all that apply

G1 Physics · Accepted Answer

By symmetry, E = 0 exactly at the centre. Take a small displacement x along a diagonal. Expanding the field of the four positive vertex charges about the centre gives E p a r a l l e l E_parallel E p ​ a r a l l e l ≈ -Kx, where K > 0. Thus for q > 0, F p a r a l l e l F_parallel F p ​ a r a l l e l = q E p a r a l l e l E_parallel E p ​ a r a l l e l ≈ -qKx, which is restoring: stable along the diagonal. For q < 0 the force reverses direction and is destabilising. Therefore A, B and C…