I Electric Potential in circuit

AI Thread Summary
The discussion focuses on the application of the electric potential formula in circuit models. The formula for electric potential at a point suggests that higher positive charge concentrations should exist where potential is higher, which contradicts the neutrality of points in a simple circuit. It is clarified that the formula applies to voltage due to point charges, not to continuous charge distributions found in circuits. The presence of a continuous distribution of surface charge complicates the application of the formula, as there are no solitary point charges in the circuit. Thus, the traditional electric potential equation does not accurately represent the behavior of circuits.
eyeweyew
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Electric potential at a point equation for circuit and net charge
I reviewed some of the fundamental physics and I looked back at the equation for Electric potential at a point p:
$$V(p) = k \sum_{i} {\frac {q_i} {r_i}}$$
where

- p is the point at which the potential is evaluated;
- ri is the distance between point p and point i at which there is a nonzero charge;
- qi is the charge at point i

and I still find it's kind of contradicting with the simple circuit model such as the one below. Both point a and point b should be neutral with no net charge so their electric field is 0 and the voltage is flat on the graph according to Gauss law. I understand the electric potential of point b is ε higher than that of point a (i.e. V(b)-V(a)=ε) means it takes ε work to move a +1 test charge from point a to point b along the circuit.

But according to Electric potential formula at a point, should that also imply there are higher positive net charge concentration around point b than point a so how can they both neutral with no net charge? Does that mean the equation for Electric potential at a point does not apply in a circuit model but if so, why?

electric_circuit_voltage_plots-001.png

image reference: https://tikz.net/electric_circuit_voltage_plots/
 
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Is that formula supposed to be the voltage at a point or the voltage due to a point charge? Read the surrounding text carefully
 
Dale said:
Is that formula supposed to be the voltage at a point or the voltage due to a point charge? Read the surrounding text carefully
It is voltage at a point due to other point charges. I edited my post to clarify it. Thanks!
 
eyeweyew said:
It is voltage at a point due to other point charges. I edited my post to clarify it. Thanks!
So that formula doesn’t really apply. There are no solitary point charges in that circuit. There is a continuous distribution of surface charge along all the conductors. That distribution doesn’t have a nice closed form expression.
 
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