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Homework Help: Simple question on Laplace's Equation (electrostatics)

  1. Oct 22, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider solutions to the One Dimensional Laplace's Equation in Cartesian Coordinates

    Let the range of x be from x1 to x2 (x1 > x2) and the boundary conditions are V[x1] = V1 and V[x2] = V2

    Find the equation for V[x]

    2. Relevant equations
    V[x] = 1/2 (V(x+a)+V(x-a))
    V[x] = mx + b

    3. The attempt at a solution
    I don't understand what equation I'm asked for.. from what I know the slope m is the difference in V over the difference in x, and the b is V2*x1 - V1x2 / x1-x2. Do I just apply that here? what about the equation V[x] = 1/2 (V(x+a)+V(x-a)) ?
    Last edited: Oct 22, 2015
  2. jcsd
  3. Oct 23, 2015 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    You are supposed to find V(x) using Laplaces equation ##\nabla^2V=0##
    Do so ... start by writing down the 1D Laplaces equ as an appropriate boundary value problem, then solve the equation normally.
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