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  5. Electric field lines

5.6 Electric field lines  (Page 3/5)

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Always keep in mind that field lines serve only as a convenient way to visualize the electric field; they are not physical entities. Although the direction and relative intensity of the electric field can be deduced from a set of field lines, the lines can also be misleading. For example, the field lines drawn to represent the electric field in a region must, by necessity, be discrete. However, the actual electric field in that region exists at every point in space.

Field lines for three groups of discrete charges are shown in [link] . Since the charges in parts (a) and (b) have the same magnitude, the same number of field lines are shown starting from or terminating on each charge. In (c), however, we draw three times as many field lines leaving the + 3 q charge as entering the − q . The field lines that do not terminate at − q emanate outward from the charge configuration, to infinity.

Three pairs of charges and their field lines are shown. The charge on the left is positive in each case. In part a, the charge on the right is negative. The field lines are represented by curved arrows starting at the positive charge on the left, curving toward and terminating at the negative charge on the right. Between the charges, the field lines are dense. In part b, the charge on the right is positive. The field lines represented by curved arrows start at each of the positive charges and diverge outward. Between the charges, the field lines are less dense, and there is a black region midway between the charges. In part c, the charge on the right is negative. The field lines start at the positive charge. Some of the lines, those that start closest to the negative charge, curve toward the negative charge and terminate there. Lines that start further from the negative charge curve toward it but then diverge outward. There is an area with very low density of lines to the right of the pair of charges.
Three typical electric field diagrams. (a) A dipole. (b) Two identical charges. (c) Two charges with opposite signs and different magnitudes. Can you tell from the diagram which charge has the larger magnitude?

The ability to construct an accurate electric field diagram is an important, useful skill; it makes it much easier to estimate, predict, and therefore calculate the electric field of a source charge. The best way to develop this skill is with software that allows you to place source charges and then will draw the net field upon request. We strongly urge you to search the Internet for a program. Once you’ve found one you like, run several simulations to get the essential ideas of field diagram construction. Then practice drawing field diagrams, and checking your predictions with the computer-drawn diagrams.

One example of a field-line drawing program is from the PhET “Charges and Fields” simulation.

Summary

  • Electric field diagrams assist in visualizing the field of a source charge.
  • The magnitude of the field is proportional to the field line density.
  • Field vectors are everywhere tangent to field lines.

Conceptual questions

If a point charge is released from rest in a uniform electric field, will it follow a field line? Will it do so if the electric field is not uniform?

yes; no

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Under what conditions, if any, will the trajectory of a charged particle not follow a field line?

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How would you experimentally distinguish an electric field from a gravitational field?

At the surface of Earth, the gravitational field is always directed in toward Earth’s center. An electric field could move a charged particle in a different direction than toward the center of Earth. This would indicate an electric field is present.

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A representation of an electric field shows 10 field lines perpendicular to a square plate. How many field lines should pass perpendicularly through the plate to depict a field with twice the magnitude?

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What is the ratio of the number of electric field lines leaving a charge 10 q and a charge q ?

10

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Problems

Which of the following electric field lines are incorrect for point charges? Explain why.

Figure a shows field lines pointing away from a positive charge. The lines are uniformly distributed around the charge. Figure b shows field lines pointing away from a negative charge. The lines are uniformly distributed around the charge. Figure c shows field lines pointing away from a positive charge. The lines are denser on the right side of the charge than on the left. Figure d shows field lines pointing toward a positive charge. The lines are uniformly distributed around the charge. Figure e shows field lines pointing toward a negative charge. The lines are uniformly distributed around the charge. Figure f shows two positive charges. Field lines start at each positive charge and point away from each. The lines are uniformly distributed at the charges and bend away from the midline. Some lines intersect each other. Figure g shows a positive 5 micro Coulomb charge and a negative micro Coulomb charge. Several field lines are shown. Long the line connecting the charges is a field line that points away from the positive charge and toward the negative one. Another field line forms an ellipse that starts at the positive charge and ends at the negative charge. Another field line also forms an ellipse that points away from the positive and ends at the negative charge but appears to envelop the charges rather than start and end at the charges.
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In this exercise, you will practice drawing electric field lines. Make sure you represent both the magnitude and direction of the electric field adequately. Note that the number of lines into or out of charges is proportional to the charges.

(a) Draw the electric field lines map for two charges + 20 μ C and −20 μ C situated 5 cm from each other.

(b) Draw the electric field lines map for two charges + 20 μ C and + 20 μ C situated 5 cm from each other.

(c) Draw the electric field lines map for two charges + 20 μ C and −30 μ C situated 5 cm from each other.


Figure a shows a positive 20 micro Coulomb charge on the left, a negative 20 micro Coulomb charge on the right, and the field lines due to the charges. The field lines come out of the positive charge and converge coming into the negative charge. The outer field lines extend beyond the drawing area and so we see them bending to the right, toward the negative charge, but only see part of the line. The density of lines coming out of the positive is the same as the density going into the negative. Figure b shows a positive 20 micro Coulomb charge on the left, a positive 20 micro Coulomb charge on the right, and the field lines due to the charges. The field lines come out of the positive charges and diverge, bending away from the far charge. The density of lines is the same near each of the charges. Figure c shows a positive 20 micro Coulomb charge on the left, a negative 30 micro Coulomb charge on the right, and the field lines due to the charges. The field lines come out of the positive charge. More lines go into the negative 20 micro Coulomb charge than come out of the positive 20 micro Coulomb charge. All of the lines coming out of the positive charge terminate at the negative, while the outer lines going into the negative start at infinity.

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Draw the electric field for a system of three particles of charges + 1 μ C , + 2 μ C , and −3 μ C fixed at the corners of an equilateral triangle of side 2 cm.

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Two charges of equal magnitude but opposite sign make up an electric dipole. A quadrupole consists of two electric dipoles are placed anti-parallel at two edges of a square as shown.

Four charges are shown at the corners of a square. At the top left is positive 10 nano Coulombs. At the top right is negative 10 nano Coulombs. At the bottom left is negative 10 nano Coulombs. At the bottom right is positive 10 nano Coulombs.

Draw the electric field of the charge distribution.


Four charges are shown at the corners of a square. At the top left is positive 10 nano Coulombs. At the top right is negative 10 nano Coulombs. At the bottom left is negative 10 nano Coulombs. At the bottom right is positive 10 nano Coulombs. The field lines are also shown. They come out of the positive charges and curve toward and end at the negative charges. The lowest density is near the center of the square.

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Suppose the electric field of an isolated point charge decreased with distance as 1 / r 2 + δ rather than as 1 / r 2 . Show that it is then impossible to draw continous field lines so that their number per unit area is proportional to E .

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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