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The Maxwell's equations for electrostatic are derived from Coulomb's law which has been formulated based on experiments. This provides initial experimental evidence for the Maxwell's equations. We discuss two applications of Maxwell's equations. The first result is that the electric field inside an empty cavity in conductors is proved to be zero. The second result is an expression for electric stress tensor is derived. The surface integral of the electric tensor gives the force on charge distribution.
Maxwell's First Equation from Coulomb's LawStarting with the Gauss law and using divergence theorem of vector calculus we derive Maxwell's first equation \(\nabla\cdot \vec{E}= \rho/\epsilon_0\). |
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Maxwell's Second Equation from Coulomb's LawClick for detailsMaxwell's equation, \(\nabla \times \vec{E}=0\), can be easily proved by direct computation of curl of electric field of a point charge and appealing to the superposition principle. |
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Electric Field Inside an Empty Cavity in a ConductorMaxwell's equation, \(\text{curl}\vec{E}=0\), is used to prove that the electric field inside an empty cavity in a conductor is zero. |
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The Electric Stress TensorAn expression for the electric stress tensor is derived for a charge distribution in a volume \(V\). The surface integral of the stress tensor gives the total electric force on the charge in the volume \(V\). |
