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Electric Field-To potential

  1. Mar 18, 2017 #1
    1. The problem statement, all variables and given/known data
    ##V = V (x,y,z) = 10^3(2x^2 + 3y^2 −5z^2 + 7x)−19999##
    Find ##V_{ba}
    ##\vec {r_a}=2i##
    ##\vec {r_b}=j+k##

    2. Relevant equations

    ##E## will be ##E=-∇V##
    ##V_b-V_a=-\int_a^b E(r)\, dr##

    3. The attempt at a solution

    When I try to calculate the potential using ##V_b-V_a=-\int_a^b E(r)dr##, and ##E=-∇V## dr I get ##-26.10^3##
    Electric field at a is ##-15.10^3i##
    Electrci Field at b is ##-6.10^3j+10.10^3k##
    so inital ##V## is ##-30.10^3 V## final ##V## is ##-4.10^3 V## from integral and thres minus sign so its ##-26.10^3 V##
    when I use ##V = V (x,y,z) = 10^3(2x^2 + 3y^2 −5z^2 + 7x)−19999## inserting here I get ##-24.10^3V##
     
  2. jcsd
  3. Mar 18, 2017 #2

    TSny

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    Homework Helper
    Gold Member

    The general expression is ##V_b-V_a=-\int_a^b \vec{E} \cdot d\vec{s}##, where the integration is along some path connecting the points a and b. The integrand involves a dot product.
    It's not clear how you did the integration. What path did you choose? Why did you evaluate ##\vec E## at the specific points a and b? The integral depends on ##\vec E## at all points of the path of integration.
     
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