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marvelous
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Why is the electric potential constant in a conductor that is at equilibrium?
Electricity(Electric potential)
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In a conductor at equilibrium, the electric potential remains constant due to the absence of electric fields within the conductor, which prevents the movement of charge carriers like electrons. If the potential were not constant, electrons would experience a force causing them to move, disrupting the equilibrium. The concept of equilibrium in this context refers to a state where the electric potential is uniform throughout the conductor. This uniformity ensures that there are no net forces acting on the electrons, maintaining stability. Therefore, the electric potential must be constant in a conductor at equilibrium to prevent charge movement and maintain a balanced state.
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sophiecentaur
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marvelous said:
I could also ask you what you mean by "equilibrium" - the definition should involve the word "potential".
I'm thinking about the following problem. I have an electrified fluid with a constant charge density, Q, within the fluid. Will this necessarily yield a surface charge?
Would I have to compute it by looking at the displacement fields on either side of the interface? Would it change if the bulk charge within the fluid remains constant?
This is from Griffiths' Electrodynamics, 3rd edition, page 352.
I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##.
In matrix form, this tensor should look like this...
Please can anyone either:-
(1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges?
Or alternatively (2) point out where I have gone wrong in my method?
I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula.
Here is my method and results so far:-
This...
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