Electric Potential and Potential Energy 
Due to Point Charges
Electric Potential and Potential Energy 
Due to Point Charges
(12.13)
(12.14)
Obtaining
the Value of the Electric Field from the Electric Potential
The potential difference dV between two points a distance ds apart
as
(12.15)
(12.16)
The equipotential surfaces must always be perpendicular to the electric field lines passing through them.
Obtaining
the Value of the Electric Field from the Electric Potential
(12.17)
The equipotential surfaces are perpendicular to field lines.
Obtaining
the Value of the Electric Field from the Electric Potential
(12.18)
Electric Potential Due to Continuous
Charge Distributions
(12.19)
(12.20)
Electric
Potential Due to a Charged Conductor 
We now show that every point on the surface of
a charged conductor in equilibrium is at the same electric potential.
The surface of any charged conductor in electrostatic equilibrium is an equipotential surface. Furthermore, because the electric field is zero inside the conductor, we conclude that the electric potential is constant everywhere inside the conductor and equal to its value at the surface.
Electric
Potential Due to a Charged Conductor 
The electric field is large near convex points having small radii of curvature and reaches very high values at sharp points.
Electric
Potential Due to a Charged 
Conductor 
A Cavity Within a Conductor
In this case, the electric field inside the cavity must be zero
(12.21)
A cavity surrounded |
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by |
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conducting walls is a field-free |
Corona Discharge |
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region as long as no charges are |
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inside the cavity. |
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