Structure of Isolines of Electric Potential

Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education

Electric fields and electric potential are closely related. In this lesson, we will explore how do draw equipotenial lines, and determine the effect of equipotential lines on a charged particle.

Field Lines

Imagine you decide to go hiking in the mountains. What do you need to bring before you head out? One item that would be extremely helpful is a topographical map that shows the elevations of the area in which you will be hiking.


Topographical map
topo

The squiggly lines drawn across the map are called contour lines or isolines. Isolines are lines that connect points of equal values. In the topographical map, points of equal elevation are connected.

Let's look at another map showing isolines. In this diagram, points of equal gravitational potential energy are connected with a line. Gravitational potential energy (GPE) is the energy of the position of a mass with respect to a reference point. Think of the floor as our reference point, and imagine a book on the floor. You pick up that book, and do work on it by moving it to the top of the bookshelf. The book now has GPE.


GPE isolines in red
grav

The red circles are the GPE isolines, and the black arrows represent the direction of force on a mass at that location. Notice that the black arrows are perpendicular to the GPE isolines.

Electric Potential

Electric potential is defined by the work that has to be done to move a charged particle in an electric field. Electric fields are created by charged particles, and always point away from positive charges, and towards negative charges. Let's say an electric field exists in between two oppositely charged plates. If we take a small negative test charge, and move it from the positive plate towards the negative plate, it will gain electric potential because it took work to move it. This is analogous to you moving the book from the floor to the top of the bookshelf.

Also, consider this analogy. Think about trying to move a hungry dog away from his food bowl. He is friendly, and won't snap at you, but it will require effort on your part to move him away from that bowl. When you have him a few feet away from the bowl, and let him go, he will be ''pulled'' back towards the bowl. The same thing happens with the electric charge in between the charged plates. Opposites attract so the negative charge wants to be at the positive plate. When it is moved away from the positive plate it gains electric potential.


Moving a charge in an electric field
efield

Drawing Isolines of Electric Potential

As mentioned previously, electric field lines always point away from positive charges, and towards negative charges. Electric potential lines can be drawn on an electric field map, but there are a few rules concerning how to draw them.

1. They are always closed loops (ending at the edge of a piece of paper or page is okay).

2. They always cross the electric field lines at right angles.

3. They can not cross any other electric potential line.

4. They are closer together where the electric field strength is greater.

5. They do not pass through a conductor.

Let's draw an equipotential map from a set of field lines. Our first step is to start with an electric field map, and in this case, it is one generated by two oppositely charged particles, as seen in the diagram, and two outside of the view of the diagram.


Black arrows point in the direction of the magnetic field, and the grey lines are the electric field lines
field1

Now, we draw little hash marks perpendicular to the field lines.


Draw the hash marks where it can be drawn perpendicular to the electric field lines
perpend

And finally, connect the perpendicular hash marks with a smooth line. This represents the isolines of electric potential.


Pink lines are the electric potential isolines
final

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