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Chapter 23c - Chapter 23 Gauss Law Part C Applications of...

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September 11, 2009 Ch. 23: Gauss' Law - Part C 1 Chapter 23: Gauss’ Law – Part C Applications of Gauss’ Law ! A point charge inside a conducting shell. ! A point charge inside conducting shells. ! Spherical symmetry. ! Two shell theorems. ! Uniform volume charge distribution. ! HITT question. ! Axial symmetry – uniformly charged cylinder.
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September 11, 2009 Ch. 23: Gauss' Law - Part C 2 A Point Charge Inside a Conducting Shell ! A point charge ( -Q ) lies inside a concentric conducting shell with radius R (black lines show the inner and the outer surface of the shell). ! The conducting shell is neutral. ! What is the charge on the inner surface of the shell? ! What is the surface charge density on the outer surface of the shell? -Q Q =0 1
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September 11, 2009 Ch. 23: Gauss' Law - Part C 3 -Q A Point Charge Inside a Conducting Shell ! We draw a Gaussian surface (sphere) within the conducting shell, that encloses the point charge and the inner surface of the shell. ! E=0 inside the conductor; the enclosed charge is zero. ! Charge on the inner surface of the shell must be +Q . ! Since the shell is neutral, and all the charges are on the surface, the charge on the outer surface must be –Q , and σ = -Q/4 π R 2 . Gaussian surface (red sphere) + + + + + + + + + + + + + + + + +Q - - - - - - - - - - - - - - - - -Q
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September 11, 2009 Ch. 23: Gauss' Law - Part C 4 A Point Charge Inside Conducting Shells ! A point charge -Q lies inside two concentric conducting shells. ! First shell (light red) has charge +2Q . ! Second shell (yellow) has charge -4Q . ! What is the charge on the outer surface of the first shell? ! What is the charge on the inner surface of the second shell? ! What is the charge on the outer surface of the second shell? -Q +2Q -4Q
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September 11, 2009 Ch. 23: Gauss' Law - Part C 5 A Point Charge Inside Conducting Shells Gaussian surface (red sphere) -Q +2Q -4Q +Q + + + + + + + + + + + + + + + + +Q + + + + + + + + + + + + + + + + ! We draw a Gaussian surface within the first conducting shell, that encloses the point charge and the inner surface of the shell.
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