Find the solution to ∇2 Ψ(r, θ, φ) = 0 inside a sphere with the following boundary conditions:
∂Ψ (1,θ,φ)=sin2θcosφ.∂r
Find the solution to ∇2 Ψ(r, θ, φ) = 0 inside a sphere with the following boundary conditions: ∂Ψ (1,θ,φ)=sin2θcosφ.∂r...
Find the solution to inside a sphere with the following boundary conditions applied to its three sides. Please give explanation. Find the solution to V24(r, e, ¢) = 0 inside a sphere with the following boundary conditions: (1, e, ) sin20 cosp ar
I am hoping with explanation to go with solving the problem, especially with regards to applying the boundary conditions correctly. Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, ) sin20 cosp = ar Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, ) sin20 cosp = ar
Please give some insight on how to apply boundary conditions. This is really important for me to understand separation of variables and how/which terms are eliminated and why. Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, ) sin20 cosp = ar Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, )...
30] Find th e solution of the following boundary value problem. 1<r<2, u(r, θ = 0) = 0, u(r, θ = π) =0, 1,0-0, u(r-2,0)-sin(20), 0 < θ < π. u(r Please also draw the sketch associated with this problem. You may assume that An -n2, Hn(s)sin(ns), n 1,2,3,. are the eigenpairs for the eigenvalue problem H(0) 0, H(T)0. 30] Find th e solution of the following boundary value problem. 1
9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u = 1 + 2 sin θ on r-R. 9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u = 1 + 2 sin θ on r-R.
1. The potential at the surface of a sphere is kept at potential V(R.0)-Vo sin20. The potential at infinity is zero. (a) Find V(r, 0) inside the sphere. (b) Find V(r,0) outside the sphere. (c) Find σ(θ), the charge density on the sphere. (d) Find the total charge of the sphere. (e) The problern would be a lot harder if the potential were specified to be V(R,θ)-Võsin θ Why? Explain how you would do part (a) without going through the...
2. Potential Inside a Sphere We are interested in the electric potential inside a spherical shell that is radius a and centered on the origin. There are no charges inside the she, so the potential satisfies the Laplace equation, However, there is an external voltage applied to the surface of the shell which holds the potential on the surface to a value which depends on θ: As a result, the potential Ф(r,0) -by symmetry, it does not depend on ф-is...
1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ 1. Evaluate the integral of f(r, θ, φ)-1 + r2 cos2( over a sphere of radius h. (Hint: we did most of this problem in class; 9) sin φ
Epsilon1=2 Epsilon0 6. In the spherical region #1 (0 r a, 0 θ π ,0 φ 2π ), the electric field just below the spherical surface r-din region # i (where espe ) is given by E,,10+ 20 + ф40 . Gue On the spherical surface at r -a there exists a uniform surface charge density Pso 8 Find 52 in region #2 just above r a. Hint: Let E,EE+0E2,
(16 pts total) The potential at the surface of a sphere of radius R is given by Vo k(35cos 0-30cos +5cos+3) where k is a constant. Assume there is no charge inside or outside the sphere. 2. a. (5 pts) Write Vo in terms of Legendre polynomials b. (6 pts) Determine the boundary conditions and find the potential inside and outside the sphere. (5 pts) Find the surface charge density σ(θ) at the surface of the sphere. C.