817.2 The calculation of the electric potential @ Find the electric potential a distance r from a spherical shell of radius r that has a charge o distributed uniformly throughout its surface for r>R and r< respectively 0 (r<R) E Q (r>R) 4 E choose V=0 E CC edr Qr·dr oc .7"y nE 0 R 兀G 817.2 The calculation of the electric potential outside 47er R E E·dr inside E =「E,drF+「Ed R Qr·drQ 4760/ 4ER 4rE,R constant O R7 1Find the electric potential a distance r from a spherical shell of radius R that has a charge Q distributed uniformly throughout its surface, for r >R and r <R respectively. r r Q r Qr r V E r P r 1 4 4 ˆ d d 0 2 0 out out = ∝ ⋅ = ⋅ = ∫ ∫ ∞ ∞ πε πε r r r ( ) 4 ˆ 0 ( ) 2 0 r R r Qr r R E > < = πε r R Q o r P r E r o 2 1 r ∝ r E R = 0 V∞ choose §17.2 The calculation of the electric potential constant 4 4 ˆ d d d d 0 2 0 in out inside ' ' = = ⋅ = = ⋅ + ⋅ = ⋅ ∫ ∫ ∫ ∫ ∞ ∞ ∞ R Q r Qr r E r E r V E r R R R P P πε πε r r r r r r r r r Q V 1 4 0 outside = ∝ πε R Q o r P r E r o 2 1 r ∝ r E R P′ r ∝ 1 o R r R Q 0 4πε V §17.2 The calculation of the electric potential