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Ch0206 - Chapter 6 The Electric Potential Due to One or...

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Chapter 6 The Electric Potential Due to One or More Point Charges 42 6 The Electric Potential Due to One or More Point Charges The electric potential due to a point charge is given by r q k = ϕ (6-1) where ϕ is the electric potential due to the point charge, k = 2 2 9 C Nm 10 99 8 × . is the Coulomb constant, q is the charge of the particle (the source charge, a.k.a. the point charge) causing the electric field for which the electric potential applies, and, r is the distance that the point of interest is from the point charge. In the case of a non-uniform electric field (such as the electric field due to a point charge), the electric potential method for calculating the work done on a charged particle is much easier than direct application of the force-along-the-path times the length of the path. Suppose, for instance, a particle of charge q ′ is fixed at the origin and we need to find the work done by the electric field of that particle on a victim of charge q as the victim moves along the x axis from x 1 to x 2 . We can’t simply calculate the work as ) ( 1 2 x x F even though the force is in the same direction as the displacement, because the force F takes on a different value at every different point on the x axis from x = x 1 to x = x 2 . So, we need to do an integral: dx F d = W dx qE d = W dx x q k q d 2 = W = 2 1 2 x x dx x q
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