How is Maxwell stress tensor calculated?

1. The force per unit volume of charge is, therefore, f =
2. = ρE + ρv × B. (3)
3. DERIVATION OF THE MAXWELL STRESS TENSOR. Consider the Lorentz force Equation (3) and use Maxwell’s equations to write.
4. μ0. ∇ × B − ϵ0∂tE.
5. × B. = [ϵ0∇ · E]E −
6. B × [∇ × B] − ϵ0∂t [E × B] + ϵ0E × ∂tB.
7. B × [∇ × B] − ϵ0∂t [E × B]
8. g × [∇ × g] = ∇

Is the Maxwell stress tensor symmetric?

The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. The latter describes the density and flux of energy and momentum in spacetime.

How many components Maxwell’s stress tensor has?

The tensor that we’ve discussed, namely the Maxwell stress tensor, is an example of a “rank-2 tensor”. In three dimensions, a rank-2 tensor can be described using 9 projections, called components, which are conveniently presented in a 3×3 matrix.

What is the purpose of the Maxwell stress tensor?

The Maxwell stress tensor is used to determine the magnetic or electrostatic force density, is the stress tensor of the magnetic field. is the stress tensor of the electrostatic field.

How is the stress tensor used in electromagnetism?

Maxwell stress tensor. The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a homogeneous magnetic field,…

Is the electrowetting force due to Maxwell stress?

The electrowetting force is due to the Maxwell stress tensor [23–25] and, because the system is static at the onset of motion, can be translated as a capillary effect using Lippmann–Young’s law. It has been established [26] that the electrowetting force during full motion from one electrode to the next is given by

Can you write f as the tensor divergence of the stress tensor?

All but the last term of f can be written as the tensor divergence of the Maxwell stress tensor, giving: