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Overview of solution methods. Simple 1-D problems. Reduce Poisson’s equation to Laplace’s equation. Capacitance. The method of images. Overview. Illustrated below is a fairly general problem in electrostatics. Many practical problems are special cases of this general problem. Where to start?
Electrostatic charges and forces problems are presented along with detailed solutions. Problems Problem 1: What is the net force and its direction that the charges at the vertices A and C of the right triangle ABC exert on the charge in vertex B?
The electrostatic potential is given as a function of x in figure (a) and (b). Calculate the corresponding electric fields in regions A, B, C and D. Plot the electric field as a function of x for the figure (b).
1.1. Vector calculus. In this problem we recall a number of standard identities of vector calculus which we will frequently use in electrodynamics. De nitions/conventions: We commonly write the well-known vectorial di erentiation op-erators grad, div, rot using the vector ~r of partial derivatives ri := @=@xi as.
Examples of Electrostatic Problems with Dielectrics Problem: Find (electric flux density), (electric field intensity), and (polarization) for a metallic sphere (radius a, charge Q), coated by a dielec-tric (radius b), and the charge densities at the interfaces. Solution: Use Gauss’ Law In region 0, In region 1, a < r < b:
So for V, we have only one 2 nd order DE to solve, but if we approach the problem using electric field q, we end up with two equations: · q L Ù, H q L Ù In general, there are two major ways to solve the potential problems in electrostatic: (a) Solve as a source problem using integration, (b) Solve as a boundary value problem, using boundary
ected. For Γ = −1, the formula gives 0, as. expected.(a) The current at a voltage maximum is zero. (b. The voltage at the short circuit ter-mination is zero. The d. stance between voltage extrema is λ/4, so λ/4 = 8. m. The distance between voltage maxima is λ/2 = 16 cm. Therefore, the distance between the short c.
