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# ch22 - Chapter 22 Electric Fields In this chapter we will...

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Chapter 22 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary, Coulomb’s law describes adequately the forces among charges. If the charges are not stationary we must use an alternative approach by introducing the electric field (symbol ). In connection with the electric field, the following topics will be covered: -Calculating the electric field generated by a point charge. -Using the principle of superposition to determine the electric field created by a collection of point charges as well as continuous charge distributions. -Once the electric field at a point P is known, calculating the electric force on any charge placed at P . -Defining the notion of an “electric dipole.” Determining the net force, the net torque, exerted on an electric dipole by a uniform electric field, as well as the dipole potential energy. (22-1) E r

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In Chapter 21 we discussed Coulomb’s law, which gives the force between two point charges. The law is written in such a way as to imply that q 2 acts on q 1 at a distance r instantaneously (“action at a distance”): Electric interactions propagate in empty space with a large but finite speed ( c = 3 × 10 8 m/s). In order to take into account correctly the finite speed at which these interactions propagate, we have to abandon the “action at a distance” point of view and still be able to explain how q 1 knows about the presence of q 2 . The solution is to introduce the new concept of an electric field vector as follows: Point charge q 1 does not exert a force directly on q 2 . Instead, q 1 creates in its vicinity an electric field that exerts a force on q 2 . 1 2 2 0 1 4 q q F r πε = 1 2 generates electric field exerts charge a force on r r r F E E q q (22-2) 1 q 1
Consider the positively charged rod shown in the figure. For every point in the vicinity of the rod we define the electric field vector as follows: We place P E Definition of the Electric Field Vector 1. r 0 0 0 a test charge at point . We measure the electrostatic force exerted on by the charged rod. We define the electric field . vector at point as: SI Units : q P F q E P F E q = 2. positiv 3 e . r r r r 0 From the definition it follows that is parallel to . We assume that the test charge is small enough so that its presence at point does not affect the charge distribution on the N/C d ro E F q P Note : r r and thus alter the electric field vector we are trying to determine. E r 0 F E q = r r (22-3)

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q q o r P E r 2 0 1 4 q E r πε = 0 0 0 Consider the positive charge shown in the figure.
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