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Calculating the electric field of a cylinder
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[QUOTE="Jolb, post: 4511163, member: 187392"] Well, first you are right that the radial force outward from the axis of the cylinder should cancel on the axis of the cylinder. One way to see this is through a basic "symmetry argument." Imagine there were a radial force away from one spot on the axis. Now imagine we rotated the problem around the axis of the cylinder. The cylinder looks exactly the same, but the radial component is pointing in another direction! We have considered the same problem but gotten different answers about the radial component, so "by symmetry" it must cancel. Another way to see this is that any radial field from one part of the cylinder at a point on the axis would be canceled out by the the radial field from the opposing spot on the cylinder (i.e. the point that is directly across the axis). Now: how to do this problem? Do you know how to calculate the electric field due to a ring of charge at a point sitting on the axis going perpendicularly through the center of the ring? Use the superposition principle to "build" the cylinder out of infinitely many rings. [/QUOTE]
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Calculating the electric field of a cylinder
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