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Continuous_charge_Gauss_Law_examples

# Continuous_charge_Gauss_Law_examples - EXAMPLE(a Find the...

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Unformatted text preview: EXAMPLE: (a) Find the electric field INSIDE and OUTSIDE of a uniformly charged insulating sphere with radius a and total charge Q. (b) Plot the magnitude of E as a function of distance r from sphere centre. (c) Calculatethe electric potential V0”) inside and outside the sphere. 15‘: Look at r < a (inside of sphere) Gaussian . _ surface . Draw Gaussran surface, radius r, / same centre . By symmetry, E is L to Gaussian surface everywhere . Normal component En is uniform over the surface E" nd. ' V \ 2 , Look at r > a (outSIde of sphere) / r . Draw Gaussian surface, radius r, same centre ( o By symmetry, 5‘ is t to /\, Gaussian surface everywhere \ l ' . Normal component E, is uniform \ _/ /i3#§é? over the surface @ 13‘: Ltooketrjg (inside of sphere) G i .W _ ousson . Draw Gaussran surface, radius r, /s/urfoce same centre ' . By symmetry, E is J. to Gaussian surface everywhere . Normal component En is uniform over the surface @- 2“d: Look at r > a (outside of sphere) e A . Draw Gaussian surface, radius r, \ same centre / . By symmetry, E is J. to ( Gaussian surface everywhere . Normal component En is uniform \ f over the surface \ / 33\$? @ /\>6'( [01/1‘5/7é) :77 ﬂ@ [DIS/W W. J u 2 _> 2 §fw€ :Enx#/7/‘ :3: w / . C? 62415? 000 g” 0 “Cr/75¢ r/2 ﬂ @ ﬁle ﬁr; Qﬂwﬁ (5) Pat—2 gnu) {if \ fr rm. (5) Parg/z/r/ﬂ“ .' 724\$ M2705: 0‘ Q “‘“" WM 1‘ F 2 _ _, luv “to“ ,éemggcég, rte f>6< .9 Wm Jami; v 00f N r (from?) [\faﬁ My]: éi - C? F CL /2 (2 z 2 More West/(aipﬂéwcﬂr ” MM” :7” (My) @ @ Q EXAMPLE: What is the magnitude of the electric field at a perpendicular distance r from an infinitely long, uniformly charged rod with charge per unit length of l ? Gaussian surface ﬂ 0 @ EXAMPLE: What is the magnitude of the electric field near an infinitely large, uniformly charged plane with charge per unit area ofa ? TE Gaussian ~w1/ surface ...
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