Question

Three charges +4q,-q and +4q are kept on a straight line at position (0,0,0),(a,0,0) and (2a,0,0) respectively. Considering that they are free to move along the x-axis only

• A. All the charges are in stable equilibrium
• B. All the charges are in unstable equilibrium.
• C. Only the middle charge is in stable equilibrium.
• D. Only middle charge is in unstable equilibrium.

Answer 1

The correct option is A All the charges are in stable equilibrium

Configuration of the charges : [Ref. image]

From symmetry and by using Columb's law $(F=\frac{k{Q}_q}{R^2})$

one can show net force on each charge is zero.______(i)

also, potential energy of system,

$u=k[\frac{\left(4q\right)(-q)}{a}+\frac{\left(4q\right)(-q)}{a}+\frac{\left(4q\right)\left(4q\right)}{2a}]$

$u=0$_____(ii)

(i) and (ii) imply ,

system is in stable equilibrium.