The superposition principle of the electric field is fundamentally based on the linearity of Maxwell's equations, as outlined in Jackson's Electrodynamics. The principle asserts that the electric field resulting from multiple sources can be calculated by vectorially adding the individual fields, which is mathematically represented by the divergence operator in the context of Gauss' law. This linearity ensures that the net electric field is equivalent to the sum of the individual fields, reinforcing the concept that forces can be added together in a linear system.
PREREQUISITESPhysicists, electrical engineers, and students of electromagnetism seeking to deepen their understanding of the superposition principle and its applications in electric fields.
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)