How Does Gauss' Law Apply to Currents in Electric Fields and Circuitry?

[Brendan Graham]

I am designing a device, which will utilize an electric field. The question I have run into is whether or not the current is treated as the charge enclosed for Gauss' Law, or if there's another way I would calculate it. Also, am I correct that the voltage of the circuit would be different than the electric potential of the electric field I am trying to create? Thanks!

 

[berkeman]

I am designing a device, which will utilize an electric field. The question I have run into is whether or not the current is treated as the charge enclosed for Gauss' Law, or if there's another way I would calculate it. Also, am I correct that the voltage of the circuit would be different than the electric potential of the electric field I am trying to create? Thanks!

Welcome to the PF.

It's a bit hard to answer your questions without seeing the geometry of what you are designing, but yes, Gauss' Law for electric fields does involve the total charge enclosed by the surface. The electric field and the potential are related by the distance of the separation of the charges. Just remember that the units of the electric field are V/m (Volts per meter), and the units of the potential are V (Volts).

https://en.wikipedia.org/wiki/Gauss'_law

 

[Brendan Graham]

Welcome to the PF.

It's a bit hard to answer your questions without seeing the geometry of what you are designing, but yes, Gauss' Law for electric fields does involve the total charge enclosed by the surface. The electric field and the potential are related by the distance of the separation of the charges. Just remember that the units of the electric field are V/m (Volts per meter), and the units of the potential are V (Volts).

https://en.wikipedia.org/wiki/Gauss'_law

Hi, thanks for the help. This doesn't exactly answer my question. I am trying to understand if the current of the circuit would be the same as the charge enclosed.

 

[berkeman]

Hi, thanks for the help. This doesn't exactly answer my question. I am trying to understand if the current of the circuit would be the same as the charge enclosed.

Depends. If the charge enclosed is not moving, then no. If the charge enclosed is moving through the surface, then maybe.

Can you offer some more details about your geometry? Or a similar geometry that we can use to talk through the details of how to do the calculations?

BTW, what is your background? Have you had integral calculus yet? Basic E&M class? If the geometry is not real simple, some integrals will likely be involved in the calculations...

 

[willem2]

Hi, thanks for the help. This doesn't exactly answer my question. I am trying to understand if the current of the circuit would be the same as the charge enclosed.

A current is not a charge, so your question really makes no sense. A further problem is that currents go through loops, but you need a surface to enclose a charge, so it isn't clear what you mean by "the charge enclosed".

Of course in many circuits there are charges present (circuits with capacitors), and they are often related to the currents in the circuits, but there is no way of saying any more about this without specifying what circuit you're thinking about.

 

[Dale]

whether or not the current is treated as the charge enclosed for Gauss' Law

No. Current and charge are different things and cannot be substituted for each other.

 

[jtbell]

A current-carrying wire is normally electrically neutral. It has equal amounts of (stationary) positive and (moving) negative charge.