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6B Ch 22-Gauss Law

6B Ch 22-Gauss Law - E = Ei Ai cos i = Ei A i lim E E = Ai...

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±²³´µ´¶ &´·¸¹º»¼¹ ½·"$ & ¾¿"ÀÀ ± À Á¿# & ÂÃ÷¼¹¿ ÄÅÀ ÄÆ ¾¿"ÀÀ ± À Á¿# &Ç²È ±²³´µ´¶ & ´$ø»¼É¸Åº¿· Ê¿À¼À ÄÆ ¾¿"ÀÀ ± À ¿ÅË ±Ä"·ÄÉÌ ± À Á¿#À ÍżºÀ ÄÆ ±Î¿Ãº¸» ''
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±²³´µ¶·´ ¸²¹º ±º»¼½²³ &&"%¾ ±²³´µ¶·´ ¿¹º À»²´¹²»µ³ µÁ³ ³²³´µ¶·´ ¿¹º µÁ¶Â¹ÃÁ µÁ³ ¶³´µ»Äò³ ÅÁÂÆÄ ÇÁ³ ¶³´µ»Äò³ ·Å %$ ´¼ ÈÉ &$ ´¼Ê µÁ³ ³²³´µ¶·´ ˳²Ì ·Å ¹Ä·Í¶¼ »µ &$$ Î! ÀÊ »ÄÌ µÁ³ »Äò³ θ ·Å '$#
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±²³´ µ¶·¸³¹¶ º »²¸¼½¾ ¼³·¿º»½À Á²½»µ·Â» ±²³´ cos Ei i ii i EA θ ΔΦ == Δ ±± lim 0 i i surface A d Δ→ Φ = ⋅Δ = E A ± ±
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Electric Flux, Interpreting the Equation • The flux is a maximum when the surface is perpendicular to the field • The flux is zero when the surface is parallel to the field • If the field varies over the surface, Φ = E A cos θ is valid for only a small element of the area
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Electric Flux, final • The surface integral means the integral must be evaluated over the surface in question • In general, the value of the flux will depend both on the field pattern and on the surface • The units of electric flux will be N . m 2 /C 2
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Electric Flux, Closed Surface • Assume a closed surface • The vectors point in different directions – At each point, they are perpendicular to the surface – By convention, they point outward i Δ A ±
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Flux Through Closed Surface, cont At (1), the field lines are crossing the surface from the inside to the outside; θ <90 o , Φ is positive At (2), the field lines graze the surface; θ =90 o , Φ = 0 At (3), the field lines are crossing the surface from the outside to the inside;180 o > θ >90 o , Φ is negative
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Flux Through Closed Surface The net flux through the surface is proportional to the net number of lines leaving the surface – This net number of lines is the number of lines leaving the volume surrounding the surface minus the number entering the volume If E n is the component of E perpendicular to the surface, then Φ E = ± E d ± A = E n dA ± ±
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Gauss ± Law, Introduction Gauss ± Law is an expression of the general relationship between the net electric flux through a closed surface and the charge enclosed by the surface – The closed surface is often called a Gaussian surface Gauss ± Law is of fundamental importance in the study of electric fields
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6B Ch 22-Gauss Law - E = Ei Ai cos i = Ei A i lim E E = Ai...

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