Question

5. Two particles carrying a charge of qi-+8q and q -2q are fixed in place: charge qi is at the origin while the charge q2 is at a distance R. A what point (other than infinitely away) can a proton be placed so that it is in equilibrium (the net force on it is zero)? Is that equilibrium stable or unstable? (That is, if the proton is displaced, do the forces drive it back to the point of equilibrium or drive it further away? qi q2

Answer 1

Let the proton is placed at distance �d� as shown To be equilibrium Net force = 0 = > 1/4 pi elementof_0 q_1/(R + d)^2 + 1/4 pi elementof_0 q_2/d^2 = 0 = > 8q/(R + d)^2 - 2q/d^2 = 0 = > 9R + d/d)^2 = 4 R + d/d = 2 R + d = 2 R + d = 2 d d = R Therefore Proton has to be placed at a distance �R� as shown in figure. And this equilibrium is unstable i.e., force drive is further away.