Find the magnitude of the potential difference between two points located \(1.4 \mathrm{m}\) apart in a uniform \(650-\mathrm{N} / \mathrm{C}\) electric field, if a line between the points is parallel to the field.

To comprehend the potential difference in an electric field, one must first understand the concept of electric field strength. Electric field strength, denoted as \( E \), measures the force per unit charge exerted by an electric field on a positively charged test particle. It is expressed in units of newtons per coulomb (\( N/C \)).

In a practical sense, the field strength signifies how strong the invisible electric field is: the greater its value, the more force it will exert on charges within it. For instance, if a charge experiences a large force in a region of space, the electric field strength in that region is said to be high. Our scenario involves a uniform electric field of \( 650 N/C \), which means that a test charge would feel a steady force of 650 newtons for every coulomb of charge, regardless of its position in the field.

When addressing the task of calculating the potential difference, or voltage, between two points in an electric field, we rely on understanding that this potential difference represents the work done to move a unit charge between those points. The calculation becomes straightforward in a uniform electric field.

The equation that ties potential difference \( V \) to electric field strength \( E \) and distance \( d \) is: \[ V = E \times d \].

This potential difference, measured in volts (V), is directly proportional to both the strength of the electric field and the distance over which the charge is moved. As the distance increases, or as the field strength increases, so too does the amount of work required to move a charge, thereby increasing the potential difference. For example, pushing against a strong wind requires more effort than pushing against a gentle breeze; similarly, more work is needed to move a charge through a stronger electric field.

Imagine a uniform electric field as a grid where the spacing between grid lines is consistent throughout, indicating equal field strength at every point. This uniformity simplifies calculations involving forces and potentials within the field since the values are constant everywhere.

A uniform electric field can be visually represented by parallel lines that show the direction of the force that a positive charge would experience. The force on any positive charge placed in a uniform field will always be in the same direction and have the same magnitude, which is a product of the charge's magnitude and the field's strength.

In the environment of a uniform field, calculating the potential difference, as seen in the provided exercise, does not require integration over space, since the electric field is not changing with position. The consistent strength throughout the field is what makes \( V = E \times d \) a valid approach for determining the potential difference between any two points aligned with the field's direction.