From what I know a battery works by moving electrons through the circuit due to the chemical potential difference between the terminals , Here I have two questions
How do we calculate the potential difference of a battery ,in electrostatic potential it's calculated by taking the negative integral of E.ds so how does this compare to the battery as I've heard multiple times that comparing batteries to electrostatics is misleading
Is the electric field constant around the circuit? , If it's then how can there be a potential difference between the terminals anyway I mean for it be constant at every point the positive terminal and negative terminal field must add up to the same value meaning that near the terminals the field is still constant but in a different direction which just means that the potentials will cancel.
excuse me if I am mistaken as I am finding a hard time with this problem.