Download Electric Potential - Engineering Physics - Lecture Slides and more Slides Engineering Physics in PDF only on Docsity!
Today’s agenda:
Electric potential of a charge distribution. You must be able to calculate the electric potential for a charge distribution.
Equipotentials. You must be able to sketch and interpret equipotential plots.
Potential gradient. You must be able to calculate the electric field if you are given the electric potential.
Potentials and fields near conductors. You must be able to use what you have learned about electric fields, Gauss’ law, and electric potential to understand and apply several useful facts about conductors in electrostatic equilibrium.
Electric Potential of a Charge Distribution
Example 1: potential and electric field between two parallel
conducting plates.
Assume V 0 <V 1 (so I have a direction to draw the electric field).
Also assume the plates are large compared to their separation,
so the electric field is constant and perpendicular to the plates.
V 0 V 1
Also, let the plates be separated E
by a distance d.
d
V Ed
Important note: the derivation of
did not require rectangular plates, or any plates at all. It works
as long as E is uniform and parallel or antiparallel to d.
In general, E should be replaced by the component of along
the displacement vector.
E
d V^ ^ E d
Example 2: A rod of length L located along the x-axis has a total
charge Q uniformly distributed along the rod. Find the electric
potential at a point P along the y-axis a distance d from the
origin.
y
x
P
d
L
dq
x dx
r
=Q/L
dq=dx
2 2
dq dx dV k k r (^) x d
L
0
V dV
What are we assuming when we use this equation?
Example 3: Find the electric potential due to a uniformly
charged ring of radius R and total charge Q at a point P on the
axis of the ring.
P
R
dQ
r
x
x
Every dQ of charge on the
ring is the same distance
from the point P.
2 2
dq dq dV k k r (^) x R
ring ring^2
dq V dV k
x R
P
R
dQ
r
x
x
(^2 2) ring
k V dq
x R
2 2
kQ V
x R
Could you use this expression for V to calculate E? Would you
get the same result as I got in Lecture 3?
You must derive an equation for the potential at the center of a ring if you need it for homework! In lecture I will show you how easy the derivation is.
Include the sign of Q to get the correct sign for V.
Homework hint: derive this equation in tomorrow’s homework!
P
r
dQ
x x R
R
ring ring 2 2 0 2 2 0 0
1 2 rdr rdr V dV (^4) x r 2 x r
R 2 2 2 2 2 2 2 0 0 0 0
Q
V x r x R x x R x
2 2 2 R
2
Q
R
2 2 2 0
Q
V x R x 2 R
P
r
dQ
x x R
Could you use this expression for V to calculate E? Would you
get the same result as I got in Lecture 3?
See your text for other examples of potentials calculated from
charge distributions, as well as an alternate discussion of the
electric field between charged parallel plates.
Remember: worked examples in the text are “testable.”
Make sure you know what Vab means, and how it relates to
V.
Vif = Vf – Vi so Vif = -Vif
Special Dispensation
For tomorrow’s homework only: you may use the equation for the
electric field of a long straight wire without first proving it:
line 0
E.
2 r
Of course, this is relevant only if a homework problem requires you
to know the electric field of a long straight wire.
You can also use this equation for the electric field outside a long
cylinder that carries charge.
Homework Hints!
In energy problems involving potentials, you may know the
potential but not details of the charge distribution that
produced it (or the charge distribution may be complex). In
that case, you don’t want to attempt to calculate potential
energy using. Instead, use U q V.
If the electric field is zero everywhere in some region, what
can you say about the potential in that region? Why?
1 2
12
q q
U k
r
PRACTICAL APPLICATION
For some reason you think practical applications are important.
Well, I found one!
Today’s agenda:
Electric potential of a charge distribution. You must be able to calculate the electric potential for a charge distribution.
Equipotentials. You must be able to sketch and interpret equipotential plots.
Potential gradient. You must be able to calculate the electric field if you are given the electric potential.
Potentials and fields near conductors. You must be able to use what you have learned about electric fields, Gauss’ law, and electric potential to understand and apply several useful facts about conductors in electrostatic equilibrium.
Equipotentials
Equipotentials are contour maps of the electric potential.
http://www.omnimap.com/catalog/digital/topo.htm docsity.com
