In this post, we will take a few cases where the Equilibrium of electric forces on charges on one line happens. In every case, there are 3 charges on one line. We will list down the specific equilibrium condition of each such case and the formula of equilibrium for that scenario.
Scenario 1 (Equilibrium of electric forces)
As shown in the figure, all 3 charges are placed on one line.
Now, q1 and q2 are like charges while Q is the unlike charge. (This means, the charge in the middle is opposite in polarity to the other 2 charges)
1 ) When the force on q1 is zero then
q2/Q = (r1 + r2)2/r12
2 ) When the force on q2 is zero then
q1/Q = (r1 + r2)2/r22
3 ) When the force on Q is zero then
q2/q1 = r22/r12
Scenario 2 (Equilibrium of electric forces)
If all three charges are like charges then the condition for the equilibrium of Q is,
q1/q2 = r12/r22