An electric field has a constant value of 4.0 ×10^3 V / m and is directed downward. The field is

step 1 Here we have a uniform electric field with a constant value of 4 .0 times 10 to the 3 volts per

An electric field has a constant value of 4.0 ×10^3 V / m...

An electric field has a constant value of $4.0 \times 10^{3} \mathrm{V} / \mathrm{m}$ and is directed downward. The field is the same everywhere. The potential at a point $P$ within this region is 155 $\mathrm{V}$ . Find the potential at the following points: $\quad$ (a) $6.0 \times 10^{-3} \mathrm{m}$ directly above $P, \quad$ (b) $3.0 \times 10^{-3} \mathrm{m}$ directly below $P, \quad$ (c) $8.0 \times 10^{-3} \mathrm{m}$ directly to the right of $P .$

An electric field has a constant value of $4.0 \times 10^{3} \mathrm{V} / \mathrm{m}$
and is directed downward. The field is the same everywhere. The potential
at a point $P$ within this region is 155 $\mathrm{V}$ . Find the potential at the following points: $\quad$ (a) $6.0 \times 10^{-3} \mathrm{m}$ directly above $P, \quad$ (b) $3.0 \times 10^{-3} \mathrm{m}$ directly
below $P, \quad$ (c) $8.0 \times 10^{-3} \mathrm{m}$ directly to the right of $P .$

Key Concepts

Directional Dependence and Sign Conventions

Understanding the sign convention and directions is crucial: moving against the electric field results in an increase in potential, while moving with the field results in a decrease. This means that positioning relative to a reference point, combined with the known direction of the field, dictates whether the electric potential at a new location is higher or lower than the reference potential.

Uniform Electric Field

A uniform electric field is one in which the magnitude and direction of the electric field remain constant at every point in space. This concept is important because it simplifies the relationship between potential difference and displacement, allowing the use of a straight-line formula without needing integration.

Electric Potential

Electric potential is a scalar quantity that represents the electric potential energy per unit charge at a specific point in an electric field. It provides an energy perspective of the electric field and helps in calculating the work done by or against the field when a charge moves from one point to another.

Relationship Between Electric Field and Potential Difference

In a uniform electric field, the change in electric potential (voltage) between two points is directly proportional to the displacement in the direction of the field, given by the equation ?V = -E · ?r. This relationship means that for every unit of distance moved in the direction of the field, the potential changes by a constant amount, and conversely, moving perpendicular to the field does not change the potential.

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