If a point charge is displaced perpendicular to a uniform...

If a point charge is displaced perpendicular to a uniform electric field, which of the following expressions is likely to be equal to the change in electrical potential energy?
a. $-q E d$
b. 0
c. $-k_{c}\left(\frac{q^{2}}{r^{2}}\right)$

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Key Concepts

Perpendicular Displacement Relative to the Electric Field

When a charge is displaced perpendicular to the direction of a uniform electric field, its movement does not have any component along the field. Consequently, no work is done by the electric field on the charge, and there is no change in its electrical potential energy.

Work and Displacement in Electric Fields

The work done by an electric field on a charge is calculated by the dot product of the force and the displacement vector. Only the component of the displacement that is parallel to the electric field contributes to the work done, and hence to the change in electrical potential energy.

Uniform Electric Field

A uniform electric field is one in which the electric field strength and direction remain constant at every point. This means that any charge placed in the field experiences the same magnitude and direction of force irrespective of its location.

Electric Potential Energy

This is the energy a charge possesses due to its position in an electric field. It quantifies the work that would be required to move the charge from a reference position to its current position within the field, or conversely, the work that could be extracted if the charge were allowed to move within the field.

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