Here's an ODE that will emerge early in Physics 330. Using separation of variables (the PDE 3. version) we can find the following equation for the radial part R(r) of the electric potential for a...
Here's an ODE that will emerge early in Physics 330. Using separation of variables (the PDE 3. version) we can find the following equation for the radial part R(r) of the electric potential for a spherically symmetric charge distribution: r2drR + 2r-R-1(1 + 1)R = O A. Test a solution of the form: R(r)-Arı + Br-(1+1) and verify that it is a solution. B. The constants A and B are determined using boundary conditions i. Imagine that the region of interest includes the origin (r-0) but is finite (e.g., points inside a spherical shell). Argue that one of the constants must be zero in this case. ii. Imagine that the region of interest does not include the origin but does extend to infinity (e.g., points outside a spherical shell) Argue that one of the constants must be zero in this case.
Here's an ODE that will emerge early in Physics 330. Using separation of variables (the PDE 3. version) we can find the following equation for the radial part R(r) of the electric potential for a spherically symmetric charge distribution: r2drR + 2r-R-1(1 + 1)R = O A. Test a solution of the form: R(r)-Arı + Br-(1+1) and verify that it is a solution. B. The constants A and B are determined using boundary conditions i. Imagine that the region of interest includes the origin (r-0) but is finite (e.g., points inside a spherical shell). Argue that one of the constants must be zero in this case. ii. Imagine that the region of interest does not include the origin but does extend to infinity (e.g., points outside a spherical shell) Argue that one of the constants must be zero in this case.