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 ry = 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 ry = 30.
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