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Electricity and Magnetism

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Equilibrium Between Two Identical Charges and a Third Charge

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Figure 1 depicts a pair of negatively charged particles, each having a charge of $-q$, arrayed along the $\hat{x}$ axis. The electric potential is zero at the origin of the $\hat{x}$ axis. If one places a charge at that point, either positive or negative, it will experience no force. Such a point is called an equilibrium point. A point at rest there will remain at rest.

Figure 1. “Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.”

However, if a charge is displaced from the equilibrium point in either direction, one of two things can happen. If the electrical forces act on it to move it back towards the equilibrium point, the equilibrium point is stable. If the electrical forces act to move it away from the equilibrium point, it is an unstable equilibrium.

A positive charge is at

equilibrium point at the origin of the x axis.

A negative charge is at

equilibrium point at the origin of the x axis.