Based on the convention concerning line density, one would reason that the electric field is greatest at locations closest to the surface of the charge and least at locations further from the surface of the charge. The field lines are closer together in the regions of space closest to the charge and they are spread further apart in the regions of space furthest from the charge. These cross-sections represent regions of space closer to and further from the source charge. Two different circular cross-sections are drawn at different distances from the source charge. Not only does the density of lines surrounding any given object reveal information about the quantity of charge on the source charge, the density of lines at a specific location in space reveals information about the strength of the field at that location. This convention is depicted in the diagram below. By surrounding a highly charged object with more lines, one can communicate the strength of an electric field in the space surrounding a charged object by the line density. Objects with greater charge create stronger electric fields. One common convention is to surround more charged objects by more lines. The conventions are simply established in order that electric field line patterns communicate the greatest amount of information about the nature of the electric field surrounding a charged object. There are a variety of conventions and rules to drawing such patterns of electric field lines. Rules for Drawing Electric Field Patterns The presence of a few lines around a charge is typically sufficient to convey the nature of the electric field in the space surrounding the lines. Because drawing such large quantities of lines tends to decrease the readability of the patterns, the number of lines is usually limited. An electric field line pattern could include an infinite number of lines. To communicate information about the direction of the field, each line must include an arrowhead that points in the appropriate direction. As such, the lines are directed away from positively charged source charges and toward negatively charged source charges. These pattern of lines, sometimes referred to as electric field lines, point in the direction that a positive test charge would accelerate if placed upon the line. Rather than draw countless vector arrows in the space surrounding a source charge, it is perhaps more useful to draw a pattern of several lines that extend between infinity and the source charge. Note that the lengths of the arrows are longer when closer to the source charge and shorter when further from the source charge.Ī more useful means of visually representing the vector nature of an electric field is through the use of electric field lines of force. Such vector arrows are shown in the diagram below. For any given location, the arrows point in the direction of the electric field and their length is proportional to the strength of the electric field at that location. Since electric field is a vector quantity, it can be represented by a vector arrow. The direction of the electric field is always directed in the direction that a positive test charge would be pushed or pulled if placed in the space surrounding the source charge. 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 distance from the source charge. This intuitive description is made precise by Stokes' theorem.In the previous section of Lesson 4, the vector nature of the electric field strength was discussed. The curl measures the density of the angular momentum of the vector flow at a point, that is, the amount to which the flow circulates around a fixed axis. In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n Assignment of a vector to each point in a subset of Euclidean space A portion of the vector field (sin y, sin x)
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