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Chapter 19 | Electric Potential and Electric Field 845
Figure 19.10 Two nonparallel plates, held at a fixed potential difference.
Now assume that the potential difference is 60 V. If the arc length along the field line labeled by A is 10 cm, what is the electric field at point A? How about point B, if the arc length along that field line is 17 cm? How would the density of the electric potential isolines, if they were drawn on the figure, compare at these two points? Can you use this concept to estimate what the electric field strength would be at a point midway between A and B?
Answer
Applying Equation. 19.36, we find that the electric fields at A and B are 600 V/m and 350 V/m respectively. The isolines would be denser at A than at B, and would spread out evenly from A to B. Therefore, the electric field at a point halfway between the two would have an arc length of 13.5 cm and be approximately 440 V/m.
19.3 Electrical Potential Due to a Point Charge
Point charges, such as electrons, are among the fundamental building blocks of matter. Furthermore, spherical charge distributions (like on a metal sphere) create external electric fields exactly like a point charge. The electric potential due to a point charge is, thus, a case we need to consider. Using calculus to find the work needed to move a test charge from a large
distance away to a distance of from a point charge , and noting the connection between work and potential , it can be shown that the electric potential of a point charge is
(19.37) where k is a constant equal to .
Learning Objectives
By the end of this section, you will be able to:
• Explain point charges and express the equation for electric potential of a point charge.
• Distinguish between electric potential and electric field.
• Determine the electric potential of a point charge given charge and distance.