Two infinitely long grounded metal plates, again at y = 0 and y
= a ,...
Two infinitely long grounded metal plates, again at y = 0 and y
= a , are
connected at x = ± b by metal strips maintained at a constant
potential
V0 and 2V0
, respectively. Find the potential inside the resulting
rectangular pipe
Solutions
Expert Solution
a little modification is here corresponding my previous
answer
Two infinitely long plates with surface temperatures maintained
at 600 K and 300 K
respectively are placed parallel to each other. Two infinitely long
radiation shields are placed
in the evacuated space between these plates. All the surfaces
mentioned above are gray and
diffuse and have an emissivity of 0.85. Determine the steady state
temperatures of the radiation
shields.
A very large conducting plate (grounded) covers the yz plane. An
infinitely long wire with constant linear charge density λ is
placed at a distance d from the plate. You can assume that the wire
is at position (x, y) = (0, d) and extends along the z
direction.
a) Draw the location of the image charge that gives V = 0 on the
conducting plate. Indicate value(s) and position(s) of the image
charge(s).
b) Determine V (x, y) where...
Consider two infinitely long wires running parallel to the x
axis, one along (x, a, 0) the other along (x, −a, 0), for −∞ < x
< ∞ and 2a is the separation between the two wires. They carry
opposite uniform charge densities +λ and −λ respectively. (a) Find
the potential at any point (x, y, z) using the origin at your
reference point so that V (0) = 0. (b) Show that the equipotential
surfaces are (generically) circular cylinders....
Again considering y'' + 4y' + 3y = 0:
(a) Solve the IVP y'' + 4y' + 3y = 0; y(0) = 1, y'(0) = α where
α > 0.
(b) Determine the coordinates (tm,ym) of the maximum point of
the solution as a function of α.
(c) Determine the behavior of tm and ym as α →∞.
2) Imagine an infinitely long hollow metal pipe with a
rectangular cross section. The four sides are placed at x = −a and
x = a, and at y = −b and y = b. The two sides on the x-axis (and
parallel to the y-z plane) are held at V = 0, the two sides on the
y-axis (and parallel to the x-z plane) are held at a constant
positive potential V = V0. Imagine that each infinite plate...
Consider an electron between two grounded conducting parallel
plates perpendicular the x axis, and intersecting x at ±a. A
particle with charge q is placed at x = a/2 between the plates.
Derive an expression for the magnitude and direction of the force
exerted on the particle. Write your answer in terms of the
parameters q and a of the problem, and use a computer if necessary
to obtain a numerical value for your answer. Computed numerical
values should be...
Given an infinitely long rod with finite radius r (not
0), which is homogeneously charged with the charge density ρ.What
material is the rod made of, conductor or dielectric?
What is the field strength on the axis? Find several reasons for
your Answer. Calculate the electric field inside and outside the
rod.
Do the same for an infinite plane and a finite sphere of
radius R
A capacitor made of conductive plates (made of metal) is aligned
as shown. The plates have a surface area of 2 x 10-1
m2 and are 0.01 m apart from each other. The capacitor
is first connected to the voltage source until it is fully charged
and produces a potential difference of V0 = 3 kV and then released from the
voltage source earlier. If between the two capacitor plates the
plastic dielectric material is inserted and fully filling the...
Two large thin metal plates are parallel and close to each other
as in figure shown above. On their inner faces, the plates have
surface charge densities of opposite signs and of magnitude
7 * 10-22 C/m2. The
negatively charged plate is on the left and the positively charged
plate is on the right.
What are the magnitude and direction of the electric field
E
(a) to the left of the plates?
» Direction: ?
Straight out of the computer...