(2.28) If k? = 0 in Helmholtz equation we get V² = 0, which is knoum as Laplace's equation, and has many applications in physics specially in electromagnetic theory. If Ý is a function of one variable only Laplace's equation reduces to an ordinary differential equation. a) In Cartesian coordinates it takes the form eral solution of this equation. = 0 find the gen- dr? %3D d b) In spherical coordinates it takes, the form 72 dr 30 find %3D the general solution in this case. c) In cylindrical coordinates it takes the form r dr = 0 dr find the general solution for this equation.
(2.28) If k? = 0 in Helmholtz equation we get V² = 0, which is knoum as Laplace's equation, and has many applications in physics specially in electromagnetic theory. If Ý is a function of one variable only Laplace's equation reduces to an ordinary differential equation. a) In Cartesian coordinates it takes the form eral solution of this equation. = 0 find the gen- dr? %3D d b) In spherical coordinates it takes, the form 72 dr 30 find %3D the general solution in this case. c) In cylindrical coordinates it takes the form r dr = 0 dr find the general solution for this equation.
Related questions
Question
Transcribed Image Text:(2.28) If k? = 0 in Helmholtz equation we get V²½ = 0, which is knoue
as Laplace's equation, and has many applications in physics specially
in electromagnetic theory. If is a function of one variable only
Laplace's equation reduces to an ordinary differential equation.
d
a) In Cartesian coordinates it takes the form
= 0 find the gen-
dr?
eral solution of this equation.
음 (+)
1 d
b) In spherical coordinates it takes, the form
72 dr
= 0 find
dr
the general solution in this case.
1 d
c) In cylindrical coordinates it takes the form
r dr
find the general solution for this equation.
Ans.
a) (x) = a¤ +b
b) v(r) = --
+b c) (r) = a lnr + b
%3D
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
