Refer to Interactive Solution 19.37 at...

Refer to Interactive Solution $19.37$ at www.wiley.com/collegel cutnell to review a method by which this problem can be solved. 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: (a) $6.0 \times 10^{-3} \mathrm{~m}$ directly above $P$, (b) $3.0 \times 10^{-3} \mathrm{~m}$ directly below $P$, (c) $8.0 \times 10^{-3} \mathrm{~m}$ directly to the right of $P$.

Refer to Interactive Solution $19.37$ at www.wiley.com/collegel cutnell to review a method by which this problem can be solved. 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:
(a) $6.0 \times 10^{-3} \mathrm{~m}$ directly above $P$,
(b) $3.0 \times 10^{-3} \mathrm{~m}$
directly below $P$, (c) $8.0 \times 10^{-3} \mathrm{~m}$ directly to the right of $P$.

Key Concepts

Relationship Between Electric Field and Electric Potential

The electric field is related to the electric potential by the negative gradient. In a uniform electric field, the change in potential between two points is given by the electric field multiplied by the displacement in the direction of the field, with a negative sign to indicate that potential decreases in the direction of the field. This relationship is essential for calculating potential differences when moving along or against the field direction, and for understanding how movement perpendicular to the field does not change the potential.

Uniform Electric Field

A uniform electric field is one in which the electric field strength and direction are consistent throughout the region. This means that the potential difference between any two points in the field depends only on the distance between them and their relative orientation with respect to the field direction. Problems set in a uniform field often allow the use of simple linear relationships to determine changes in potential over a distance.

Electric Potential

Electric potential is a scalar quantity that represents the potential energy per unit charge at a point in an electric field. It is measured in volts (V) and indicates how much work is required to move a charge from one point to another within an electric field. The potential at a point is determined by both the magnitude of the field and the relative position of the point within the field.

Electric Field

An electric field is a region in space where a charged particle experiences a force. It is defined as the force per unit charge and is a vector quantity, meaning it has both magnitude and direction. In problems involving electric fields, the field lines indicate the direction that a positive test charge would move, and the field strength determines how much force the charge would experience over a certain distance.

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