P4. Consider the collinear arrangement of three charges shown. (a) Determine so that equilibrium exists. +2q...

Find the change Q: Given that the system can be considered to be in equilibrium, i.e the total force acting on 'Q' is zero. Force is given by the formula, F = 1/4 pi epsilon_0 q_1 q_2/r^2 r^^where q_1 and q_2 are the charges and r is the separation between them for charge 'Q' due to + 2q [left] the force can be calculated as F_1 = 1/4 pi epsilon_0 2qQ/r^2 (-i^^) Since opposite charges attract each other for charge 'Q' due to '+ 2q' (on the right), the force can be calculated as, I_2 = 1/4 pi epsilon_0 2qQ/r^2 (i^^) Since the forces are separated by 180 degree, the consultant force, _net squareroot F^2_1 + F^2_2 - F_1 F_2 cos (180 degree) F_net = squareroot F_1^2 + F_2^2 - F_1 F_2 Because cos 180 degree = -1 F_net = squareroot (F_1 - F_2)^2 = F_1 - F_2 Therefore F_net = 1/4 pi epsilon_0 2qQ/r^2 (-i^^) - 1/4 pi