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gauss questions - Gauss' Law Although the electric field of...

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Gauss' Law Although the electric field of any given charge distribution can be calculated using Coulomb's Law (as we did last week), the method involves the evaluation of integrals, which, to put it mildly, is tedious. Happy Happy Joy Joy there exists another method of calculating the electric field, which relies on a theorem called Gauss' Law. This law is a consequence of Coulomb's Law and there is no new physics but it does contain some new math which provides an elegant shortcut for calculating the electric field of a charge distribution PROVIDED that the distribution has a certain amount of symmetry. Gauss' Law doesn't work in all cases but when it does it is wondrous. However, we need first to introduce a new concept: Electric Flux Electric Flux and the number of field lines Consider a mathematical (that is, imagined surface in the shape of a rectangle of area A that is immersed in a constant electric field E. This electric field makes an angle θ with the surface and therefore has a component tangential to the surface and a component normal, that is perpendicular, to the surface. The electric flux Φ though the surface is defined as the product of the area A by the magnitude of the normal component of the electric field Φ = E n A = E A cos θ The quantity A cos θ can be seen as the projection of the area A onto a plane perpendicular to the electric field, that is, A cos θ can be regarded
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as that part of the area A the faces the electric field 'head on.' Now the magnitude of the electric field must be proportional to the magnitude of the charge, the number of field lines that we draw coming out of a (positive) charge must be proportional to the charge. There is a convention that the number of field lines coming out of a charge Q is Q/ ε o - so the number of field lines coming out of a coulomb of charge is 1/
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gauss questions - Gauss' Law Although the electric field of...

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