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Science · Advanced Physics
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4422:56 6 fieldandwaveelectromagneticsd-1412... t to 3-3 Coulombs Law 83 Let us consider the simple case of an electrie dipole that consists of a pair of equal and opposite charges +q and -4, separated by a small distance, d, as shown in Fig. 3-5. Let the center of the dipole coincide with the origin of a spherical coor- dinate system. Then the E field at the point P is the sum of the contributions due to +g and-4. Thus, (3-23) The first term on the right side of Eq. (3-23) can be simplified ifd « R. We write 21-3/2 (3-24) where the binomial expansion has been used and all terms containing the second and higher powers of (d/R) have been neglected. Similarly, for the second term on the right side of Eq. 3-23) we have 2 R Substitution of Eqs. (3-24) and (3-25) in Eq. (3-23) leads to (3-26) t4 +d/2 FIGURE 3-5 Electric field of a dipole.

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