How Do You Know the Direction of the Electric Field

Electric Field Lines

In the previous section of Lesson 4, the vector nature of the electric field forcefulness was discussed. The magnitude or strength of an electric field in the space surrounding a source charge is related directly to the quantity of charge on the source charge and inversely to the altitude from the source accuse. The direction of the electrical field is always directed in the direction that a positive test charge would exist pushed or pulled if placed in the space surrounding the source charge. Since electric field is a vector quantity, it can be represented by a vector pointer. For whatsoever given location, the arrows point in the management of the electric field and their length is proportional to the force of the electric field at that location. Such vector arrows are shown in the diagram below. Note that the lengths of the arrows are longer when closer to the source accuse and shorter when further from the source charge.

A more useful means of visually representing the vector nature of an electrical field is through the use of electric field lines of strength. Rather than draw endless vector arrows in the infinite surrounding a source charge, it is peradventure more useful to depict a pattern of several lines that extend between infinity and the source charge. These blueprint of lines, sometimes referred to equally electric field lines , signal in the direction that a positive examination charge would accelerate if placed upon the line. As such, the lines are directed away from positively charged source charges and toward negatively charged source charges. To communicate data about the management of the field, each line must include an arrowhead that points in the appropriate direction. An electric field line blueprint could include an infinite number of lines. Considering drawing such large quantities of lines tends to subtract the readability of the patterns, the number of lines is usually limited. The presence of a few lines effectually a charge is typically sufficient to convey the nature of the electrical field in the infinite surrounding the lines.

Rules for Drawing Electrical Field Patterns

There are a variety of conventions and rules to drawing such patterns of electric field lines. The conventions are simply established in gild that electric field line patterns communicate the greatest amount of data about the nature of the electric field surrounding a charged object. I common convention is to surroundings more charged objects by more lines. Objects with greater charge create stronger electric fields. Past surrounding a highly charged object with more lines, one can communicate the strength of an electrical field in the infinite surrounding a charged object by the line density. This convention is depicted in the diagram below.

Not only does the density of lines surrounding whatever given object reveal information about the quantity of accuse on the source accuse, the density of lines at a specific location in space reveals information about the strength of the field at that location. Consider the object shown at the right. Two different round cantankerous-sections are fatigued at different distances from the source accuse. These cross-sections stand for regions of space closer to and further from the source charge. The field lines are closer together in the regions of space closest to the charge; and they are spread further autonomously in the regions of space furthest from the charge. Based on the convention concerning line density, 1 would reason that the electric field is greatest at locations closest to the surface of the accuse and least at locations further from the surface of the accuse. Line density in an electric field line blueprint reveals information about the strength or magnitude of an electric field.

A second rule for drawing electric field lines involves drawing the lines of force perpendicular to the surfaces of objects at the locations where the lines connect to object'southward surfaces. At the surface of both symmetrically shaped and irregularly shaped objects, in that location is never a component of electric force that is directed parallel to the surface. The electric force, and thus the electric field, is always directed perpendicular to the surface of an object. If at that place were e'er whatsoever component of force parallel to the surface, then whatsoever excess charge residing upon the surface of a source charge would brainstorm to accelerate. This would lead to the occurrence of an electric current within the object; this is never observed in static electricity. Once a line of force leaves the surface of an object, it will often alter its management. This occurs when cartoon electric field lines for configurations of ii or more charges every bit discussed in the section beneath.

A terminal rule for drawing electric field lines involves the intersection of lines. Electric field lines should never cross. This is particularly important (and tempting to suspension) when cartoon electric field lines for situations involving a configuration of charges (as in the section below). If electric field lines were ever allowed to cross each other at a given location, and so yous might be able to imagine the results. Electric field lines reveal information about the direction (and the forcefulness) of an electric field inside a region of space. If the lines cross each other at a given location, then there must exist ii distinctly dissimilar values of electric field with their own private direction at that given location. This could never be the case. Every single location in infinite has its ain electric field strength and direction associated with it. Consequently, the lines representing the field cannot cross each other at any given location in space.

Electrical Field Lines for Configurations of Two or More Charges

In the examples in a higher place, we've seen electric field lines for the space surrounding single point charges. Simply what if a region of space contains more than ane bespeak charge? How can the electric field in the space surrounding a configuration of 2 or more charges be described by electric field lines? To respond this question, we will first render to our original method of drawing electric field vectors.

Suppose that there are ii positive charges - charge A (Q_A) and charge B (Q_B) - in a given region of space. Each charge creates its ain electrical field. At whatever given location surrounding the charges, the force of the electric field tin exist calculated using the expression kQ/dⁱⁱ. Since in that location are two charges, the kQ/d² calculation would take to be performed twice at each location - once with kQ_A/d_A ² and once with kQ_B/d_B ² (d_A is the altitude from that location to the eye of charge A and d_B is the distance from that location to the center of charge B). The results of these calculations are illustrated in the diagram below with electric field vectors (E_A and Due east_B) drawn at a variety of locations. The strength of the field is represented by the length of the arrow and the direction of the field is represented by the direction of the pointer.

Since electrical field is a vector, the usual operations that employ to vectors can be applied to electric field. That is, they can exist added in head-to-tail fashion to decide the resultant or net electric field vector at each location. This is shown in the diagram below.

The diagram in a higher place shows that the magnitude and direction of the electric field at each location is simply the vector sum of the electrical field vectors for each private accuse. If more locations are selected and the process of cartoon E_A, Due east_B and Due east_internet is repeated, then the electric field forcefulness and direction at a multitude of locations will exist known. (This is not washed since it is a highly fourth dimension intensive job.) Ultimately, the electrical field lines surrounding the configuration of our 2 charges would begin to emerge. For the limited number of points selected in this location, the beginnings of the electric field line pattern tin can be seen. This is depicted in the diagram below. Notation that for each location, the electric field vectors point tangent to the direction of the electrical field lines at whatever given point.

The construction of electrical field lines in this manner is a tedious and cumbersome task. The utilize of a field plotting computer software program or a lab procedure produces similar results in less fourth dimension (and with more phun). Whatever the method used to determine the electrical field line patterns for a configuration of charges, the general thought is that the pattern is the resultant of the patterns for the individual charges within the configuration. The electrical field line patterns for other charge configurations are shown in the diagrams below.

In each of the above diagrams, the private source charges in the configuration possess the same amount of charge. Having an identical quantity of accuse, each source accuse has an equal ability to change the space surrounding information technology. Subsequently, the pattern is symmetrical in nature and the number of lines emanating from a source charge or extending towards a source accuse is the same. This reinforces a principle discussed before that stated that the density of lines surrounding any given source charge is proportional to the quantity of charge on that source accuse. If the quantity of charge on a source charge is not identical, the pattern will take on an asymmetric nature, as one of the source charges will accept a greater ability to alter the electrical nature of the surrounding space. This is depicted in the electric field line patterns below.

Afterwards plotting the electrical field line patterns for a variety of charge configurations, the general patterns for other configurations tin can exist predicted. There are a number of principles that volition assist in such predictions. These principles are described (or re-described) in the list beneath.

• Electric field lines always extend from a positively charged object to a negatively charged object, from a positively charged object to infinity, or from infinity to a negatively charged object.
• Electric field lines never cross each other.
• Electric field lines are near dumbo around objects with the greatest amount of charge.
• At locations where electric field lines meet the surface of an object, the lines are perpendicular to the surface.

Electric Field Lines as an Invisible Reality

It has been emphasized in Lesson 4 that the concept of an electrical field arose every bit scientists attempted to explain the action-at-a-distance that occurs between charged objects. The concept of the electric field was get-go introduced by 19th century physicist Michael Faraday. Information technology was Faraday'southward perception that the blueprint of lines characterizing the electric field represents an invisible reality. Rather than thinking in terms of one charge affecting some other accuse, Faraday used the concept of a field to propose that a charged object (or a massive object in the case of a gravitational field) affects the infinite that surrounds information technology. Every bit another object enters that space, it becomes affected by the field established in that space. Viewed in this manner, a charge is seen to interact with an electric field every bit opposed to with some other charge. To Faraday, the hole-and-corner to understanding activeness-at-a-distance is to understand the power of accuse-field-charge. A charged object sends its electric field into infinite, reaching from the "puller to the pullee." Each charge or configuration of charges creates an intricate web of influence in the space surrounding it. While the lines are invisible, the issue is always so real. And then as you practice the exercise of constructing electric field lines around charges or configuration of charges, you are doing more than simply cartoon curvy lines. Rather, yous are describing the electrified web of space that volition describe and repel other charges that enter it.

We Would Like to Suggest ...

Sometimes it isn't enough to just read about it. You have to interact with it! And that'southward exactly what you exercise when you use 1 of The Physics Classroom's Interactives. We would similar to advise that you combine the reading of this page with the use of our Put the Charge in the Goal Interactive and/or our Electric Field Lines Interactive. Both Interactives can be establish in the Physics Interactives section of our website. Both Interactives provide engaging environments for exploring electric field lines.

Check Your Agreement

Use your understanding to respond the following questions. When finished, click the button to view the answers.

one. Several electric field line patterns are shown in the diagrams beneath. Which of these patterns are incorrect? _________ Explain what is wrong with all incorrect diagrams.

two. Erin Agin drew the following electric field lines for a configuration of two charges. What did Erin do wrong? Explain.

iii. Consider the electric field lines shown in the diagram below. From the diagram, it is apparent that object A is ____ and object B is ____.

a. +, +

b. -, -

c. +, -

d. -, +

due east. bereft info

4. Consider the electric field lines drawn at the right for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in society of the electric field strength - from smallest to largest.

v. Use your understanding of electric field lines to identify the charges on the objects in the post-obit configurations.

6. Observe the electrical field lines below for various configurations. Rank the objects according to which has the greatest magnitude of electric accuse, start with the smallest charge.

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Source: https://www.physicsclassroom.com/class/estatics/Lesson-4/Electric-Field-Lines

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