why do electric field lines goes inward for negative charge and outwards for positive charge

Asked by  | 26th Mar, 2009, 05:02: PM

Expert Answer:

Following describes how to draw electric field lines with the helpof geometry and their directions.

A simple picture probably helps. You can use the following diagrams to place a charge on screen and see it's electric field. The first diagram shows the field as vectors which give the direction of the field at various points in space (projected into two dimensions!). The second diagram is a 3-dimensional view of test particles (i.e. small particles each with an infinitesimal positive charge and mass) moving in response to the electric field of the particle placed on the screen. Place more than one charge on the screen to see the electric field due to several point charges.

The program shows the correct convention for drawing electric field lines. The field lines are a characterization of the actual electric field. The field extends radially, in all directions in 3-dimensional space, from the charge. If the charge is positive, the field is said to point away from the charge. If the charge is negative, the field points in towards the charge. The field lines give a general idea of the direction, but it is important to remember that the actual field in 3 dimensions extends to every point in space out to infinity if there are no other charges or matter.

The weird shape of the field for two or more charges comes about strictly for geometrical reasons. The electric force, we find experimentally, is both conservative and obeys the principal of superposition (just as gravitational forces do). Therefore, electric fields must also obey these rules. The superposition property means that electric fields from two different sources add vectorially to produce a net field. The four possible combinations of positive or negative charges are shown.

 


Vector components for electric fields from two charges.

 

Note that we have chosen the same position (relative to the charges) to calculate the net electric field in each of the four cases. For cases 1 and 2 (both charges the same sign), we note that the horizontal or x components of the fields tend to cancel, leaving the y components to add. This will be true for any point which is close to the line which is parallel to y and located at an x position close to the midpoint between the charges. If you look at the diagram, you should note that the field lines indicate that the field is nearly vertical for points close to the midpoint line as we have described it. For cases 3 and 4 (unlike charges), the position we have chosen for calculating the net electric field tends to have the y components canceling and the x components adding. Hence any point near the midpoint line for unlike charges will have electric fields pointing nearly horizontally. Right along the midpoint line, the y component is exactly zero (assuming the two charges are equal magnitude).

To draw the field lines for two charges as in the diagram, we need to find the vector sum of the electric fields extending radially from or toward each charge (depending on whether the charge is positive or negative) at each point in space, then, for some small subset of points, find the direction of the net electric field. The field lines in the diagram show the general direction of the electric field for various positions around the charges. Thus, the shape looks complex, but it is arrived at by doing the vector sum of radial field lines from each charge, so nothing complex is going on.

Answered by  | 26th Mar, 2009, 08:38: PM

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