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Chapter23 Electrical potential
1.1
Electric potential energy
• Electric force (elasticity, gravity) is a conservative force. ∆U + ∆K = 0
(work done by a conservative force doesn’t depends on the path taken,
but only on the initial and final positions)
R ~r
~ ~l
• ∆U = −∆K = −We = − ~r12 Eqd
• Electric potential energy in a uniform field
∆U = −∆K = −We = −Eq(xf − xi )
• Electric potential energy for two point charges U = ke q1rq2
Example 23.1
• Electric potential energy for multiple point charges:
The potential energy for a collection of charges q1 , q2 , q3 ...,
P
q q
U = ke i<j riijj
Example 23.2
The potential energy for a charge q0 in the presence of a collection of
charges q1 , q2 , q3 ...,
P qi
U = ke q0
ri
• unit: J
1.2
Electric potential
• Electric potential is potential energy per unit charge ∆V =
∆U
q
• Unit Joule per Coulomb, J/C or Volt, V
R ~r
~ ~l
• ∆V = − ~r12 Ed
∆V = −E(xf − xi )
There is another way to calculate E, unit could be N/C or V/m
• Due to a point charge U = ke qq
r
V = ke rq , V=0 when r− > ∞
E = ke rq2
• Due to multiple charges, superposition principle
The potential for a charge q0 in the presence of a collection of charges
q1 , q2 , q3 ...,
P qi
V = qU0 = ke
ri
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• Due to a charge distribution Va −Vb =
Rb
a
~ ~l =
Ed
Rb
a
Ecosφdl = −
Ra
b
Ecosφdl
HW3.6
• electron volt (eV), the kinetic energy that an electron gains when accelerated through a potential difference of 1V.
1eV = 1.6 × 10−19 C.V = 1.6 × 10−19 J
1.3
Equipotential surface
• Charged conductor in electrostatic equilibrium: electric potential is constant everywhere inside a conductor and equal to the same value at the
surface. VA = VB , W = 0
• No work is required to move a charge at constant speed on an equipotential
surface.
• Electric field is perpendicular to the equipotential surface.
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