Field lines are a visual representation of a mathematical construct, like a graph of a function. The defining properties of this visual representation are. The second property tells you that the field lines can never cross. If they did the density at the point where they crossed would be infinite, and the implication would be that the field strength is infinite.
This is unphysical. Here is one more way to think about it. What would it mean for two field lines to cross at a particular point? It would mean that the field had two different directions at that point.
The principle of superposition tells us that the net field is simply the vector sum of the two. So the total field would only have one line going through the same point with a direction which was given by the sum of the two other directions.
A positive particle accelerates along the electric field lines. If it came to an intersection, what way should it go? Two electric fields line can never cross each other because at every point there is unique tangential direction of electric Fields. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?
Learn more. Ask Question. Asked 7 years, 7 months ago. Active 1 year, 4 months ago. What is the force between two small charged spheres having charges of 2 x 10 —7 C and 3 x 10 —7 C placed 30 cm apart in air?
Calculate the magnitude of the torque acting on the dipole. The charge on a proton and an electron are numerically equal i. In a macroscopic scale the number of charges used is enormous as compared to the magnitude of charge. That is, a field line cannot have sudden breaks. Why not? The charge is moving continuously from point to point rather than jumping from one point to another and experiences continuous force in the electrostatic field.
The force experienced, or the path followed by charge cannot be discontinuous and hence the lines are not broken. 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. 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.
Line density in an electric field line pattern 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's surfaces.
At the surface of both symmetrically shaped and irregularly shaped objects, there 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 there were ever any component of force parallel to the surface, then any excess charge residing upon the surface of a source charge would begin 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 direction. This occurs when drawing electric field lines for configurations of two or more charges as discussed in the section below.
A final rule for drawing electric field lines involves the intersection of lines. Electric field lines should never cross. This is particularly important and tempting to break when drawing 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, then you might be able to imagine the results. Electric field lines reveal information about the direction and the strength of an electric field within a region of space. If the lines cross each other at a given location, then there must be two distinctly different values of electric field with their own individual direction at that given location.
This could never be the case. Every single location in space has its own electric field strength and direction associated with it. Consequently, the lines representing the field cannot cross each other at any given location in space.
In the examples above, we've seen electric field lines for the space surrounding single point charges. But what if a region of space contains more than one point charge? How can the electric field in the space surrounding a configuration of two or more charges be described by electric field lines? To answer this question, we will first return to our original method of drawing electric field vectors.
Each charge creates its own electric field. The results of these calculations are illustrated in the diagram below with electric field vectors E A and E 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 arrow. Since electric field is a vector, the usual operations that apply to vectors can be applied to electric field.
That is, they can be added in head-to-tail fashion to determine the resultant or net electric field vector at each location. This is shown in the diagram below. The diagram above shows that the magnitude and direction of the electric field at each location is simply the vector sum of the electric field vectors for each individual charge.
If more locations are selected and the process of drawing E A , E B and E net is repeated, then the electric field strength and direction at a multitude of locations will be known. This is not done since it is a highly time intensive task. Ultimately, the electric field lines surrounding the configuration of our two charges would begin to emerge.
For the limited number of points selected in this location, the beginnings of the electric field line pattern can be seen. This is depicted in the diagram below. Note that for each location, the electric field vectors point tangent to the direction of the electric field lines at any given point. The construction of electric field lines in this manner is a tedious and cumbersome task. The use of a field plotting computer software program or a lab procedure produces similar results in less time and with more phun.
Whatever the method used to determine the electric field line patterns for a configuration of charges, the general idea is that the pattern is the resultant of the patterns for the individual charges within the configuration.
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