Gauss’s Law
Electric Flux
Gauss’s Law
Conductors in Electrostatic Equilibrium
Electric Flux
Electric flux is proportional to the number of electric
filed lines penetrating a surface.
Φ E = EA
Φ E = EA cosθ
→→
ΦE = E A
1
Electric flux through a curved
surface
n
→
→
Φ E ≈ ∑ Ei ⋅∆ Ai
i=1
→
→
ΦE = ∫ E ⋅ d A
Electric flux through a closed
surface
→
→
ΦE = Ñ
∫ E⋅d A
Flux entering the enclosed
volume is negative whereas flux
leaving the volume is positive.
2
The net flux through a closed surface is NOT zero only
if one or more lines start or end within the surface (the
surface encloses a net charge).
Gauss’s Law
→
→
Ñ∫ E ⋅ d A =
Qenclosed
ε0
Any difference between the input and output flux of the electric
field over any surface is due to charge within that surface.
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Conductors in electrostatic equilibrium
When there is no motion of charge within a conductor, the
conductor is in electrostatic equilibrium.
Properties:
- the electric field is zero everywhere inside the conductor
- if an isolated conductor carries a charge, the charge resides
on the surface
Conductors in electrostatic equilibrium
Properties:
3. The electric field just outside a charged conductor is
perpendicular to the surface of the conductor and has a
magnitude σ/ε0, where σ is the surface charge density at
that point
4. On an irregularly shaped conductor,
the surface charge density is greatest
at locations where the radius of
curvature of the surface is smallest
4
Infinite plane of charge
→
Qencl σ A
=
ε0
ε0
→
Ñ∫ E ⋅ d A = 2 EA =
E=
σ
2ε 0
Conducting surface
→
Qencl σ A
=
ε0
ε0
→
Ñ∫ E ⋅ d A = EA =
E=
σ
ε0
Conductor with charge inside a cavity
Suppose a conductor carries
a net charge +Q and
contains a cavity inside of
which resides a point charge
+q. What is the charge on
the inner and outer surfaces
of the conductor?
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