Find Electric Potential by integrating the electric field.

[Fabio010]

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

 

[Mentz114]

I don't think so. E_x may be a function of x,y,z.

 

[liviuct]

By definition, 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.

 

[Fabio010]

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.

 

[Chestermiller]

Here's another version of the analysis:

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

= -E_xdx -E_ydy -E_zdz