I Why Can Tzz in Maxwell's Stress Tensor Be Non-Zero in Electrostatics?

AI Thread Summary
Tzz in Maxwell's stress tensor indicates a force per unit area in the z direction, even when the electric field along z is zero in electrostatics. This component reflects the interaction of the electromagnetic field on opposite sides of a surface, rather than a force acting on a charge distribution. The analogy of a box demonstrates that applying forces in the x and y directions can still create pressure in the z direction on the top and bottom surfaces. This highlights the complexity of electromagnetic forces and their effects in electrostatic conditions. Understanding this concept is crucial for analyzing forces in electromagnetic fields.
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In summary Tzz in maxwells stress tensor represents a force per unit area in the z direction acting on an area element that is oriented along the z direction also why it could be non zero eventhough the electric field along z is zero and I'm talking here in electrostatic
 
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It is not a force on a charge distribution. It is the force of the EM field on one side of the surface acting on the EM field on the other side.
 
Orodruin said:
It is not a force on a charge distribution. It is the force of the EM field on one side of the surface acting on the EM field on the other side.
Can I use the analogy with a box when you apply forces on x and y directions on its sides but not on the top and bottom there will be pressure on the z direction on the top and bottom
 

Thread 'Maxwell stress tensor'

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...
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Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

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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