Energy in electric field
If a charge is moved between two points in an electric field, work is usually done. To be specific consider the simple field. If a positive test charge q is moved along path a from B to C, over most of the distance the motion will be against a component of the outward force due to the field and work will have to be done by some outside agency to move the charge. It is one of the most important properties of the static electric field that this work is independent of path taken. Thus the work needed to move q from B to C along b is exactly the same as that charge moves back from C to B, work will along path or work will be done on it by the field, so that either it will accelerate along the path or work will be done on some agent which prevents it from gaining speed. This work will be moving it from gaining speed. This work will be move it from B to C. the students will note that this situation is analogous to that of a mass moved in a gravitational field. Since the work done in raining an object to a higher altitude. Similarly when work is done by an outside agency to move a test charge between two points in an electric field, potential energy is stored up. For this reason the static electric is stored up. For this reason the static electric field is called a conservative field, and the law of conservation field, and law of conservation of energy applies to the movement of charged bodies in such a field. Since the work needed to move a charge between two given points in a steady field is always the same, and since the work is proportional to the charge moved, it is fruitful to use these facts to define a property of the two points in the field, namely, the electrical potential difference between points.
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