potential energy. and conservation of energy useful in our study of mechanics. In this section concepts are just as useful for understanding and interactions. reviewing several essential points from Chapters 6 and Facts on a particle that moves from point a to point e by the force is given by a line integral: 5 displacement along the particle’s path and F and diat each point along the path. force F is conservative. as we defined the term in done by F can always be expressed in terms of a V. When the particle moves from a point where the V. to a point where it is Vb the change in potential V and the work W+b done by the force is from a high point (a) to a lower point (b) under the influence force of gravity does positive work, and the gravitational When a ball is thrown upward, the gravitational force does ascent, and the potential energy increases. Third, the work-energy theorem says that the change in during any displacement is equal to the total work done on the done on the particle is done by conservative forces.


Let’s look at an plenitude and the component of displeasure ward) direction of the force The y-component of the electric force, electrical example of these basic concepts. In Fig. parallel metal plates sets up a uniform, downward electric field exerts a downward force with’ magnitude F = q, on a positive the charge moves downward a distance d from point a to point charge is constant and independent of its location. So the work done is the product of the force ma F, = -q, is constant component. This is exactly analogous to the gravitational force earth’s surface; for this force, there is a constant y-component F, = z-components are zero. Because of this analogy, we can conclude on%by the uniform electric field in Fig. 24-1 is conservative, just force. This means that the work Wa-+. done by the field is independent particle takes from a to b. We can represent this work with a pot V,just as we did for gravitational potential energy in Section 7-2.

for the gravitational force F,=-mg was V=mgy hence the potential tric force F, = -q, is

When Ya is greater than y. (Fig. 24-2a), the positive test charge the same direction as E; the displacement is in the same direction so the field does positive work and V decreases. (In particular, if y. = Fig. 24-1, Eq. (24-6) gives W’-+b  , in agreement with Eq. less than y. (Fig. 24-2b), the positive test charge moves upward, in to E; the displacement is opposite the force, the field does increases.

If the test charge is negative, the potential energy increases the field and decreases when it moves against the field (Fig. 24-3). Whether the test charge is positive or negative, the following V increases if the test charge q. moves in the direction opposite.


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