Sign of a Potential Difference

CLAIMED BY DYLAN AMADOR (FALL '16)

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Introduction

Recall from previous sections that the change in potential energy is equal to the charge times the change in potential difference. From Conservation of Energy, we know that an increase in potential energy is related to a decrease in kinetic energy, and vice versa. Furthermore, recall that the change in potential energy, potential difference, kinetic energy, etc. can be positive or negative.

Direction of Path vs. Direction of Electric Field

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors. Furthermore, it is important to note that the electric field and displacement vectors are multiplied by the dot product. Because of this dot product, we will analyze 3 different scenarios: path in the direction of the electric field, path in the opposite direction of the electric field, and the path moving perpendicular to the direction of the electric field.

Indicating Path Direction (sign convention)

Consistent with previous convention, the delta symbol indicates "final - initial." We will use this same notation in showing the direction of the path.