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notes10 2317

# notes10 2317 - ECE 2317 Applied Electricity and Magnetism...

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Prof. David R. Jackson ECE Dept. Fall Spring 2011 Notes 10 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism

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Gauss’s Law Gauss’s Law x y z q E S (closed surface) q N flux lines ˆ S D n dS q = Ñ The charge q is inside the surface. Hence N S = N ( all flux lines go through S ) S q N N Ψ = q / N = flux per line
Gauss’s Law (cont.) Gauss’s Law (cont.) N S = 0 q S ˆ 0 S D n dS = Ñ The charge q is now outside the surface (All flux lines enter and then leave the surface.) Hence

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To summarize both cases, ˆ encl S D n dS Q = Ñ By superposition, this law must be true for arbitrary charges. Gauss’s Law (cont.) Gauss’s Law (cont.) Carl Friedrich Gauss Gauss’s law
Example Example - q q 2 q S 1 S 2 1 2 ˆ ˆ 0 S S D n dS q D n dS = = Ñ Ñ Note: The charge 2 q produces E on S 1 and S 2 even though it does not appear on the RHS of Gauss’s law. Note: E 0 on S 2 !

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Using Gauss’s Law Using Gauss’s Law Gauss’s law can be used to obtain the electric
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notes10 2317 - ECE 2317 Applied Electricity and Magnetism...

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