z-gauss-homog-sphere-neuc

# z-gauss-homog-sphere-neuc - r r r> R Q 1 V(r)= 4πε r 2...

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Uniformly charged sphere tot. charge = Q R r r Q1: what is the electric field for r>R Q2: what is the electric field for r<R Q3: what is the electric potential V(r) for r>R Q3: what is the electric potential V(r) for r<R Note V(r) must be continuous Note V(r= )=0 sph-1

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Uniformly charged sphere 3 Q ρ= 4 πR 3 charged density tot. charge R r 1 in 0 Q E dA= ε i 2 2 0 Q E 4πr = ε 1 0 ρr E = r 2 3 1 2 1 0 4 (ρπr ) 3 E 4πr = ε 2 0 2 Q E = 4πε r 1 3 0 r Q E = 4πR ε { r> R r< R 2 0 Q 4πε r 3 0 r Q 4πR Rε E = or 2 0 Q r 4πε R R = 2 2 0 Q R ( ) 4πε R r = E-field sph-2
Uniformly charged sphere tot. charge = Q R r r 2 0 Q r E= 4πε R R 2 2 0 Q R E= ( ) 4πε R r E-field sph-3

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Uniformly charged sphere R r 1 r V(r)=- E dr r 2 r> R r< R 2 3 0 Q r V(r)=- +C 4πε 2R V(r)=- E dr + C 0 Q 1 V(r)= ( ) 4πε r r=R 2 3 0 0 Q 1 Q R ( ) =- +C 4πε R 4πε 2R 0 Q 3 C= 4πε 2R 2 2 0 Q 1 r V(r)= {3- } 4πε 2R R { r> R r< R V(r)= 0 Q 1 ( ) 4πε r 2 2 0 Q 1 r {3- } 4πε 2R R potential sph-4
Uniformly charged sphere R

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Unformatted text preview: r r r> R Q 1 V(r)= ( ) 4πε r 2 2 Q 1 r V(r)= {3-} 4πε 2R R tot. charge = Q potential sph-5 Uniformly charged sphere tot. charge = Q R r r 2 Q r E= 4πε R R 2 2 Q R E= ( ) 4πε R r Q 1 V(r)= ( ) 4πε r 2 2 Q 1 r V(r)= {3-} 4πε 2R R potential E-field sph-6 Uniformly charged sphere tot. charge = Q R r r 2 2 Ze r F= 4πε R R 2 2 2 Ze R F= ( ) 4πε R r 2 Ze 1 U(r)= ( ) 4πε r 2 2 2 Ze 1 r U(r)= {3-} 4πε 2R R Potential Energy Force Place charge e at r sph-7...
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## This note was uploaded on 04/03/2012 for the course PHY 1020 taught by Professor Kodera during the Spring '11 term at University of Florida.

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z-gauss-homog-sphere-neuc - r r r> R Q 1 V(r)= 4πε r 2...

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