Find Electric Potential by integrating the electric field.

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Homework Help Overview

The discussion revolves around finding the electric potential \( V(x,y,z) \) by integrating the electric field components \( E_x, E_y, E_z \). Participants are exploring the relationship between the electric field and electric potential, particularly how to approach the integration process.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning whether to integrate each component of the electric field separately or to consider the relationship between them. Some suggest that \( V \) should be derived from the sum of the integrals of all three components, while others express uncertainty about the implications of integrating just one component.

Discussion Status

The discussion is active, with various interpretations being explored regarding the integration of the electric field components. Some participants have provided insights into the definitions and relationships involved, suggesting that the potential may indeed be a combination of the integrals of the electric field components.

Contextual Notes

There is an ongoing debate about the dependencies of the electric field components on the variables \( x, y, z \), which may affect the integration approach. Participants are also considering the implications of the gradient relationship between electric field and potential.

Fabio010
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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
 
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I don't think so. Ex may be a function of x,y,z.
 
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.
 
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.
 
Here's another version of the analysis:

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

= -Exdx -Eydy -Ezdz
 

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