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Find Electric Potential by integrating the electric field.

  1. Oct 23, 2012 #1
    My question is:

    If you have a E= Ex+Ey+Ez


    To find V(x,y,z), i should:

    Just integrate Ex in order x?

    ∂V(x,y,z)/∂x = -Ex so:

    -V(x,y,z) = ∫Exdx

    or have i to sum the three integrals?

    -V(x,y,z) = ∫Exdx + ∫Eydy +∫Ezdz
     
  2. jcsd
  3. Oct 23, 2012 #2

    Mentz114

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    Gold Member

    I don't think so. Ex may be a function of x,y,z.
     
  4. Oct 23, 2012 #3
    By definiton, E(x,y,z)=-grad V(x,y,z). This means that Ex(x,y,z)=-dV(x,y,z)/dx, so just Ex will be - integral of Ex*dx. V(x,y,z) will be the sum of the three integrals, in respect to the three components of the E vector.
     
  5. Oct 23, 2012 #4
    I thought that by knowing one of the components of the vector field, i could discover the electric potential.

    So it is the sum of the three integrals:

    -V(x,y,z) = ∫Exdx + ∫Eydy +∫Ezdz


    Thanks for the answers.
     
  6. Oct 25, 2012 #5
    Here's another version of the analysis:

    dV = (∂V/∂x)dx + (∂V/∂y)dy + (∂V/∂z)dz

    = -Exdx -Eydy -Ezdz
     
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