Download Spherical Capacitor

Spherical Capacitor
Conducting sphere of radius a surrounded concentrically
by conducting spherical shell of inner radius b.
• Q: magnitude of charge on each sphere
• Electric field between spheres: use Gauss’ law
Q
Q
E[4πr2 ] =
⇒ E(r) =
0
4π0 r2
• Electric potential between spheres: use V (a) = 0
–
»
Z r
Z r
1
Q
Q
dr
1
−
V (r) = −
E(r)dr = −
=
2
4π0 a r
4π0 r
a
a
• Voltage between spheres:
Q b−a
4π0 ab
• Capacitance for spherical geometry:
ab
Q
= 4π0
C≡
V
b−a
−Q
V ≡ V+ − V− = V (a) − V (b) =
+Q
b
a
E
tsl106 – p.1/1