Phys2212_L05 - Physics 2212 Electricity and Magnetism...

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Physics 2212 Electricity and Magnetism Lecture 5 E-fields and Charged Particles in E-Fields
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10/06/09 Physics 2212 - Lecture 5 2 E-Field of a Charged Sphere Therefore, the electric field outside the surface of a uniformly spherically charged shell of charge Q with radius R is : sphere 2 0 1 ˆ 4 Q E r r πε = r sphere. The electric field inside the spherical-shell is zero (because the sum of the forces cancel). If η = Q/4 field of an infinite plane of charge. (Why?) (independent of R)
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10/06/09 Physics 2212 - Lecture 5 3 Example : A Charged Sphere A sphere with a radius R = 0.1 m has a charge Q = 20.0 nC on its surface. What is the electric field at a distance of 1.0 m from the sphere? Note that the electric field does not depend on the radius of the sphere (because the E-field of a charged sphere is the same as that of the same charge at a point at the center of the sphere.) Measuring the external E-field tells you the charge but not the radius of the sphere. sphere 2 0 9 2 2 -8 2 2 1 4 (9.0 10 N m /C )(2.0 10 C)/(1.0 m) 1.8 10 N/C Q E r πε = = × × = ×
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10/06/09 Physics 2212 - Lecture 5 4 A Parallel-Plate Capacitor The parallel plate capacitor is an important component of electronic circuits. It is constructed of two oppositely charged electrodes separated by a small gap. The net charge of the capacitor is zero. We can model the parallel plate capacitor as two parallel infinite charged planes placed a distance d apart. Let the x axis go from + to -. Then we have only to superpose the fields that we have previously calculated. We find that in the two regions outside the gap the superposed fields cancel to give 0, while in the gap they add. Therefore: outside 0 0 ˆ ˆ / 2 / 2 0 E E E i i η ε + - = + = - = r r r gap 0 0 ˆ ˆ 2 / 2 / E E E i i η ε + - = + = = r r r capacitor 0 ˆ / , so E Q Q A i A = = r
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10/06/09 Physics 2212 - Lecture 5 5 Capacitor Edge Effects Since the electrodes of a real parallel plate capacitor are not infinite, there are “edge effects” at the ends of the electrodes.
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This note was uploaded on 06/07/2009 for the course PHYSICS 2212 taught by Professor Geist during the Fall '09 term at Georgia Perimeter.

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Phys2212_L05 - Physics 2212 Electricity and Magnetism...

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