GaussLaw - Gauss’s Law The equation for Gauss’s Law is...

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Unformatted text preview: Gauss’s Law The equation for Gauss’s Law is E = Q in /A ε ₀ (where ε ₀ = 9 × 10 ⁻ ¹² ), but using it is tricky. For each of the three major shapes—planes, cylinders (including lines), and spheres—an imaginary Gaussian surface encloses them at a distance from the center r and the amount of charge inside that surface is used in the calculation, hence the Q in (though this nearly always ends up expressed in terms of charge densities ρ , σ , and λ ). The area of the surface is A , and it must be understood that the direction of the field is ± ˆ x for planes, and ± ˆ r —meaning radially outward or inward from the center—for everything else. When every possible case is analyzed, six distinct results emerge. For an infinite plane, the electric field vector is E = ˆ x σ / 2 ε . For an infinite line charge, E = ˆ r λ / 2 π r ε . The other four possible situations require more thought. Their general solutions are shown in the table to the right, based on...
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