Take the Laplacian in cylindrical coordinates and show that Poisson’s equation holds in this example.
Take the Laplacian in cylindrical coordinates and show that Poisson’s equation holds in this example.
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I have parts A & B. I just need help with c. The figure is attached.
For the cylinder of uniform charge density in Fig. 2.26:
(a) show that the expression there given for the field inside the cylinder follows from Gauss’s law
My Answer:
p = rho
r<a: E = (p*r)/ (2 * epsilon not)
r>a: E = (p * a^2)/(2 * epsilon * r)
(b) find the potential φ as a function of r, both inside and outside the cylinder, taking φ = 0 at r = 0.
My Answer:
r<a: φ(r) = (-p * r^2)/(4 * epsilon not)
r>a: φ(r) = (-p * a^2)/(4 * epsilon not) - (p * a^2)/(2 * epsilon not)(In(r/a))
c) Take the Laplacian in cylindrical coordinates and show that Poisson’s equation holds in this example.
Transcribed Image Text:E
E
a
pa?
E =
outside
pr inside
E =.
2€,
Figure 2.26.
The field inside and outside a uniform cylindrical
distribution of charge.
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