817.2 The calculation of the electric potential Q Find the electric potential a distance r from the center of a sphere of radius r that has charge o distributed uniformly throughout its volume, forr >R and r<R, respectively r<R E=arE R R Vowie-jEu dr-J Are y? choose v =0 CC- 4 817.2 The calculation of the electric potential E·dr Q R En·dF+「EdF RQr:d,rQ·dr 4 0 R 4兀Enr If we choose R V=0.v inside 十 4E。R3224zEnR 4E。2R 3-02) As shown in Fig. 17.20 88 2Find the electric potential a distance r from the center of a sphere of radius R that has a charge Q distributed uniformly throughout its volume, for r >R and r <R, respectively. ( ) 4 ˆ ( ) 4 2 0 3 0 ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ > < = r R r Qr r r R R Q E πε πε r r r r Q r Qr r V E r P r 1 4 4 ˆ d d 0 2 0 outside out = ∝ ⋅ = ⋅ = ∫ ∫ ∞ ∞ πε πε r r r = 0 V∞ choose Q R O r P §17.2 The calculation of the electric potential Q R O r P (3 ) 4 2 1 4 ) 2 2 ( 4 4 ˆ d 4 d d d d 2 2 0 0 2 2 3 0 2 0 3 0 in out inside ' ' R r R Q R R r Q R Q r Qr r R Qr r E r E r V E r R R r R R P P = − = − + ⋅ + ⋅ = = ⋅ + ⋅ = ⋅ ∫ ∫ ∫ ∫ ∫ ∞ ∞ ∞ πε πε πε πε πε r r r r r r r r r As shown in Fig.17.20 §17.2 The calculation of the electric potential If we choose VO=0,Vinside=?