Unformatted text preview: It is a hyperbola VB is for the potential outside
the sphere parabolic
joins smoothly with VB The curve for VD is for the
potential inside the sphere V for a Uniformly
Charged Sphere, Graph Continuous Charge Distributions Electric Potential for a Continuous
Charge Distribution The potential at some
point due to this charge
element is Treat it as a point charge Consider a small charge
element dq Electric Potential for a Continuous
Charge Distribution – alt. V for a Continuous
Charge Distribution, cont V for continuous charge distribution For r < R, For r > R, A solid sphere of radius R
and total charge Q V for a Uniformly
Charged Sphere Charged Conductors V Due to a
Charged Conductor This value for V uses the reference of
V = 0 when P is infinitely far away from
the charge distributions For V, you need to integrate to include the
contributions from all the elements V for a Continuous
Charge Distribution, cont V Due to a
Charged Conductor
is always perpendicular
to the displacement
Then,
Therefore, the potential
difference between A and B
on the surface is also zero Calculate field The ring has a radius a
and a total charge Q P on the perpendicular
central axis of the
uniformly charged ring V for a Uniformly
Charged Ring Thus, the surface of any charged conductor in
electrostatic equilibrium is an equipotential
surface
Because E is zero inside the conductor, V is
constant inside the conductor and equal to the
value at the surface V = 0 between any two points on the surface V is constant on the surface of a charged
conductor in equilibrium V Due to a
Charged Conductor, cont where Potential from the
infinitesimal ring V for a Uniformly Charged Disk Therefore, a cavity surrounded by conducting
walls is a fieldfree region as long as no
charges are inside the cavity E inside does not depend on the charge
distribution on the outside surface of the
conductor
For all paths between A and B, Cavity in a Conductor, cont The effect of a charge on the space
surrounding it:
The charge sets up a vector E
which is related to the force
The charge sets up a scalar V
which is related to the energy V is a function of 1/r
E is a function of 1/r2 E Compared to V Then, E is large near the
convex points having small radii
of curvature and reaches very
high values at sharp points And low where the radius of
curvature is large Charge density is high where
the radius of curvature is small Irregularly Shaped Objects Why? E inside the conductor
must be zero Given an arbitrarily shaped
cavity inside a conductor
and that no charges inside
the cavity: Cavity in a Conductor ...
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 Fall '10
 OlehTretiak
 Charge, Electric charge, conductor

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