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christian0710
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Hi if you have a galvanic cell, with Zink at the anode and Cu at the catode, which force then makes Zn electrons go to the cobber catode?
A question regarding batteries
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In a galvanic cell with zinc at the anode and copper at the cathode, the driving force for the flow of electrons from zinc to copper is the electromotive force (EMF) generated by the chemical reactions occurring at each electrode. Zinc undergoes oxidation, releasing electrons, while copper undergoes reduction, accepting those electrons. This electron flow is facilitated by the potential difference created by the differing electrode potentials of zinc and copper. The overall process is governed by the principles of electrochemistry, where the spontaneous reaction generates electrical energy. Understanding these forces is essential for applications in batteries and electrochemical cells.
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire.
We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges.
By using the Lorenz gauge condition:
$$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$
we find the following retarded solutions to the Maxwell equations
If we assume that...
Maxwell’s equations imply the following wave equation for the electric field
$$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2}
= \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$
I wonder if eqn.##(1)## can be split into the following transverse part
$$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2}
= \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$
and longitudinal part...
The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing.
The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##.
But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
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