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feynman1
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Isn't the superposition principle of electric field just force being addable? Jackson's electrodynamics says it's based on the premise of linear Maxwell's equations. Which support(s) the superposition principle?
Thanks. I think you disagree with force being addable being the basis of superposition of electricity. If Maxwell's equations were nonlinear, forces would still be generally addable yet the vector sum of forces wouldn't be the correct net force, but rather just another force.etotheipi said:If something is linear, e.g. Gauss' law, then $$\nabla \cdot (\mathbf{E}_1 + \mathbf{E}_2) = \nabla \cdot \mathbf{E}_1 + \nabla \cdot \mathbf{E}_2$$ So really if you have ##\nabla \cdot \mathbf{E}_1 = \frac{\rho_1}{\epsilon_0}## and ##\nabla \cdot \mathbf{E}_2 = \frac{\rho_2}{\epsilon_0}## then you also have ##\nabla \cdot (\mathbf{E}_1 + \mathbf{E}_2) = \frac{\rho_1 + \rho_2}{\epsilon_0}##
It's the same principle that let's you superpose two solutions to the wave equation.
"Linear" is the technical term for "addable": f (a+b) = f(a) + f(b)feynman1 said:Isn't the superposition principle of electric field just force being addable? Jackson's electrodynamics says it's based on the premise of linear Maxwell's equations. Which support(s) the superposition principle?
feynman1 said:Thanks. I think you disagree with force being addable being the basis of superposition of electricity. If Maxwell's equations were nonlinear, forces would still be generally addable yet the vector sum of forces wouldn't be the correct net force, but rather just another force.
Yes. So do you think linear Maxwell is exactly equivalent to net force being equal to the vector sum of forces?A.T. said:"Linear" is the technical term for "addable": f (a+b) = f(a) + f(b)
The superposition principle of electric field states that the total electric field at a point in space is equal to the vector sum of the individual electric fields produced by each source charge.
The superposition principle of electric field was first proposed by French physicist Charles-Augustin de Coulomb in the 18th century. It was later refined and expanded upon by other scientists, including Michael Faraday and James Clerk Maxwell.
The superposition principle of electric field is a fundamental principle in electromagnetism and is used to calculate the electric field at any point in space. It allows for the prediction and understanding of complex electric fields produced by multiple sources.
Yes, the superposition principle of electric field is only valid for linear systems. In non-linear systems, the electric field may not be directly proportional to the source charges, and the principle may not hold.
The superposition principle of electric field is similar to the principle of superposition in other fields, such as mechanics and optics. It states that the total effect at a point is equal to the sum of the individual effects produced by each source, allowing for the analysis of complex systems.