Introductory Physics Volume Two

56 Electric Potential 2.9
§ 2.9 Summary
Definitions
Electric Potential:
Capacitance:
∆V = ∆U
q
C =
Q
∆V
Equipotential: an equipotential is a surface over which the electric
potential is a constant.
Theorems
dV = − ⃗ E · ⃗dr
∆V = −
∫ rf
r i
⃗ E · ⃗ dr
[ ∂V
⃗E = −
∂x î + ∂V
∂y ĵ + ∂V ]
∂z ˆk
≡ − ⃗ ∇V
Conductors in Equilibrium:
• Field - the field is zero in the volume of a conductor, and at the
surface it is normal to the surface.
• Charge - the net charge in the volume of a conductor is zero.
• Potential - the potential in the volume of a conductor is constant.
Electric Potential of a Point Charge:
V = 1 q
4πɛ o r
Electric Potential of a Distributed Charge:
V (⃗r) = 1 ∫
dq
4πɛ o |⃗r − ⃗r s |
Energy Density of an Electric Field
E = 1 2 ɛ oE 2
Energy Stored on a Capacitor:
U = 1 2 CV 2 C