Therefore,the potential difference between the two conducting shells is: (5.2.10) which yields for the capacitance Q =4πe0 ab C (5.2.11) I△VI b-a The capacitance C depends only on the radii a and b. An "isolated"conductor (with the second conductor placed at infinity)also has a capacitance.In the limit where b→∞，the above equation becomes ab lim C=lim b-a lim4πeo 4πeoa (5.2.12) Thus,for a single isolated spherical conductor of radius R,the capacitance is C=4πeoR. (5.2.13) The above expression can also be obtained by noting that a conducting sphere of radius R with a charge O uniformly distributed over its surface has V=O/4eR,where infinity is the reference point at zero potential,V()=0.Using our definition for capacitance, C=0 Q -=4πeR. (5.2.14) I△V|Q/4πeoR As expected,the capacitance of an isolated charged sphere only depends on the radius R. 5.3 Storing Energy in a Capacitor A capacitor can be charged by connecting the plates to the terminals of a battery,which are maintained at a potential difference AV called the terminal voltage. 5-85-8 Therefore, the potential difference between the two conducting shells is: 2 0 0 0 1 1 4 4 4 b b b a r a a Q dr Q Q b a V V V E dr !" r !" a b !" ab $ % $ # % & = # = # = # = # ' # ( = # ' ( ) * ) * + + , (5.2.10) which yields for the capacitance 0 4 | | Q ab C V b a !" # $ = = % & ' ) ( * . (5.2.11) The capacitance C depends only on the radii a and b. An “isolated” conductor (with the second conductor placed at infinity) also has a capacitance. In the limit where b " ! , the above equation becomes 0 0 0 lim lim 4 lim 4 4 1 b b b ab a C a b a a b !" !" !" #$ #$ #$ % & = ' ( = = * ) + % & ' ) ( * + . (5.2.12) Thus, for a single isolated spherical conductor of radius R, the capacitance is 0 C = 4!" R . (5.2.13) The above expression can also be obtained by noting that a conducting sphere of radius R with a charge Q uniformly distributed over its surface has 0 V = Q / 4!" R , where infinity is the reference point at zero potential, V (!) = 0 . Using our definition for capacitance, 0 0 4 | | / 4 Q Q C R V Q R !" !" = = = # . (5.2.14) As expected, the capacitance of an isolated charged sphere only depends on the radius R. 5.3 Storing Energy in a Capacitor A capacitor can be charged by connecting the plates to the terminals of a battery, which are maintained at a potential difference !V called the terminal voltage