Homework Statement
A sphere of radius a with a total charge q uniformly distributed on the surface and the sphere spins with an angular velocity w
Find the electric dipole moment of the sphere/electric field outside the sphere/magnetic dipole moment of the sphere/magnetic induction outside the...
Homework Statement
The question is Jackson's 5.35. Insulated coil on a sphere (radius a) to generate uniform field B0 in the z-direction inside the sphere and dipole field outside the sphere. Conductivity is \sigma and permeability is \mu. 1st question is to find the surface current K and...
Homework Statement
This problem is at Griffiths 4.13. A very long cylinder of radius a with a uniform polarization perpendicular to the axis. The question is to solve for the field inside the cylinder.
Homework Equations
\rho_b=P\cdot\hat{n} and \sigma_b=-\nabla\cdot P
The Attempt...
Homework Statement
Known formula:J_0(k\sqrt{\rho^2+\rho'^2-\rho\rho'\cos\phi})=\sum e^{im\phi}J_m(k\rho)J_m(k\rho')
I can't derive to next equation which is e^{ik\rho\cos\phi}=\sum i^me^{im\phi}J_m(k\rho)
Homework Equations
Can anyone help me? Thanks a lot!
The Attempt at a Solution
Homework Statement
In solving a question I got a problem of solving the following integral. Your comments are appreciated.
Homework Equations
\int_{-1}^{1}xP_l'(x)dx=?
The Attempt at a Solution
I tried to solve by integration by parts, i.e...
Homework Statement
I have problems solving the related Laplace equations in the problem
Homework Equations
\frac{1}{\rho}\frac{\partial}{\partial\rho}\rho\frac{\partial g_m(\rho,\rho^')}{\partial\rho}-m^2g_m(\rho,\rho^')}=-4\pi\frac{\delta(\rho-\rho^')}{\rho}
The Attempt at a...
I know that this question was posted before but I just couldn't get it using another way around. So your comments are highly appreciated. In the textbook, \nabla\bullet\left(\widehat{r}/r^{2}\right)=4\pi\delta^{3}\left(r\right). But when I want to calculate the divergence using Catesian...