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Electricity and Magnetism

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Energy Equilibrium States of a System of Four Charges

EANDM-4HES21

Figure 1 depicts three identical charges, each of charge $q = + 2.22 \; \rm{\mu C}$, arranged at the corners of a triangle.

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

The base of the triangle has a length of $a = 10.0 \text{ cm}$ and the height of the triangle is $h = 8.41 \text{ cm}$. The field point $A$ lies along the central axis of the triangle, a distance $y = 2.5 \text{ cm}$ above the triangle’s base.

You may verify that the electric field at point $A$ is equal to zero ​so that no electric force will act upon a charge placed there. Thus, a charged particle at this point is in static equilibrium. Consider, however, infinitesimally small changes to the location of the field point.

If a positively charged particle, charge $q^\prime$, is placed at point $A$, this is a point of

equilibrium with respect to vertical displacements (along the $y$ direction).