# Find Electric Potential by integrating the electric field.

1. Oct 23, 2012

### 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

2. Oct 23, 2012

### Mentz114

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

3. Oct 23, 2012

### liviuct

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.

4. Oct 23, 2012

### 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

5. Oct 25, 2012

### Staff: Mentor

Here's another version of the analysis:

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

= -Exdx -Eydy -Ezdz