7-42. Determine the potential function for the two- dimensional flow field if V, and are known....
We can combine the scalar potential V and the vector potential A
to a combined 4-vector potential:
Calculate the components of a 4x4 electromagnetic field
tensor:
with the contravariant vector:
from the electric field
and the magnetic field
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1) A particle with mass m moves under the influence of a
potential field . The
particle wave function is stated by:
for
where and
are
constants.
(a) Show that is not time
dependent.
(b) Determine as the
normalization constant.
(c) Calculate the energy and momentum of the particle.
(d) Show that
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The stream function for an incompressible, two- dimensional flow field is v-ay-by where a and b are constants. a) Is this an irrotational flow? Governing Equation:
Assume t=0 for the following wavefunction,
, then
, and show with the potential energy function V =
that the wavefunction has definite energy
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Let V be a finite-dimensional vector space and let T L(V) be an operator. In this problem you show that there is a nonzero polynomial such that p(T) = 0. (a) What is 0 in this context? A polynomial? A linear map? An element of V? (b) Define by . Prove that is a linear map. (c) Prove that if where V is infinite-dimensional and W is finite-dimensional, then S cannot be injective. (d) Use the preceding parts to prove...
The stream function for a given two-dimensional flow field is w = 11x²y- (11/3)y3 Determine the corresponding velocity potential. Denote the constant of integration C. 4- (11x) ' - ( 11x) +C Edie
Let V be a finite dimensional inner product space,
w1,w2V. Let
TL(V)
and Tv=<v,w1>w2 for all vV.
Find all eigenvalues and the corresponding eigenspaces of T. Please
provide full solution.
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***PLEASE NOTE: I have already calculated the potential and need
help with Electric Field and induced charge at the boundaries for
this problem***
An infinitely long rectangular metal pipe (sides and ) is grounded, but
one end, at x = 0, is maintained at a specified potential , as
indicated in Fig. 3.22. What is the ELECTRIC FIELD and INDUCED
CHARGE on all boundaries? I have already worked you the potential,
and got:
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W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
A two dimensional incompressible flow is given by the velocity field V = 3yi + 2xj, in arbitrary units. Does this flow satisfy continuity? If so, find the stream function ψ(x,y) and plot a few streamlines, with arrows.