Problem 2: The expression of electric potential in cylindrical coordinates is given as V (p, Ø, z) = 3p²z sin ø. Determine the (a) numerical value of the voltage at point P(p = 1,¢ = 30°, z = 3), (b) the electric field at point P(p = 1,¢ =30°, z = 3), and (c) verify the Laplace's equation. Note: The Laplace's equation in cylindrical is expressed as: 1 a2v + az? av v?v = p ap = 0 %3D ap p2 a62
Problem 2: The expression of electric potential in cylindrical coordinates is given as V (p, Ø, z) = 3p²z sin ø. Determine the (a) numerical value of the voltage at point P(p = 1,¢ = 30°, z = 3), (b) the electric field at point P(p = 1,¢ =30°, z = 3), and (c) verify the Laplace's equation. Note: The Laplace's equation in cylindrical is expressed as: 1 a2v + az? av v?v = p ap = 0 %3D ap p2 a62
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Transcribed Image Text:Problem 2:
The expression of electric potential in cylindrical coordinates is given as
V (p, 4, z) = 3p²z sin ø. Determine the (a) numerical value of the voltage at point
P(p = 1,¢ = 30°, z = 3), (b) the electric field at point P(p = 1,ø =30°,
z = 3), and (c) verify the Laplace's equation.
%3D
Note: The Laplace's equation in cylindrical is expressed as:
()
1 a²v
+
p² ap²
av
v²v
= 0
p ap
ap
az?
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