Just as Fouriers law and the heat balance can be employed to characterize temperature distribution, analogous relationships

Question:

Just as Fourier’s law and the heat balance can be employed to characterize temperature distribution, analogous relationships are available to model field problems in other areas of engineering. For example, electrical engineers use a similar approach when modeling electrostatic fields. Under a number of simplifying assumptions, an analog of Fourier’s law can be represented in one-dimensional form as

Where D is called the electric flux density vector, e = permittivity of the material, and V = electrostatic potential. Similarly, a Poisson equation for electrostatic fields can be represented in one dimension as

Where r_y = charge density. Use the finite-difference technique with ∆x = 2 to determine V for a wire where V(0) = 1000, V(20) = 0, e = 2, L = 20, and r_y = 30.