Recent content by Nitacii

  1. Nitacii

    Find the field inside and outside a spherical geometry

    That's why I utilised the Hertz vectors, this automatically sets the correct dependence the on ##\theta##. If we reconstruct the vector potential ##\mathbf{A}## we get $$ \mathbf{A} = \nabla \times \boldsymbol{\Pi} = - \sin \theta \frac{\partial}{\partial r} \Pi_z(r,t) \hat{\boldsymbol{\phi}} =...
  2. Nitacii

    Find the field inside and outside a spherical geometry

    So I tried to solve this using the Hertz potentials. I choose the magnetic one since this one corresponds to the magnetisation. Before I start let me note that I denote a unit vector with a hat, while ##{x,y,z}## are the Cartesian coordinates and ##{r,\theta,\phi}## are the spherical...
  3. Nitacii

    Integrate source terms for test EM field in Kerr spacetime

    For clarity I finished the calculation using rules for Spin-Weighted Spherical harmonics and corrected a typo. I've modified the notebook and the pdf. But the problem of course remains.
  4. Nitacii

    Integrate source terms for test EM field in Kerr spacetime

    Hello, the Homework Statement is quite long, since it includes a lot of equations so I will rather post the as images as to prevent mistypes. We need to find the integral where with $$ J_m =(\sqrt{2}(r−ia\cos⁡θ))^{−1} i(r^2+a^2)\sin⁡(θ)j, $$ $$ J_n = - \frac{a \Delta}{ 2 \Sigma} \sin(\theta...
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