Maxwell’s Equations are a set of four equations that govern all of electromagnetism. The equations show a unification of the electric and magnetic fields and are often considered one of the greatest unifications in physics, describing one of the four fundamental interactions, the electromagnetic force. The unification of the electric and magnetic forces in the 19th century by Maxwell’s Equations led to several scientific advancements – including an entire new branch of physics, electromagnetism – and inventions that transformed the world, consequently providing the world with wide-ranging improvements in quality of life, communications and navigation.
William Gilbert, an English physicist ...view middle of the document...
Despite being named after James Maxwell, the four equations are actually simplifications of Maxwell’s original twenty equations by Oliver Heaviside. Written in partial differential form, the equations are as followed: ∇•D=ρv (1), ∇•B=0 (2), ∇xE=-∂B/∂t (3) and ∇xH=j+∂D/∂t (4), where D refers to the electric flux density, E refers to the electric field, B refers to the magnetic flux density, H refers to the magnetic field and ρv refers to the electric volume charge density. The flux densities can be related to the electric fields by D= εE and B= μH, where ε is the permeability of the electric field and μ is the permeability of the magnetic field. The symbol ∇• is the divergence operator, which is a measure of the vector flow outwards from a surface surrounding a point. Contrastingly, the symbol ∇• is the curl operator, which measures the rotation of a vector field. All four equations, despite appearing complex, can be explained in a relatively intuitive manner.
The first of Maxwell’s Equations, Gauss’ Law, states that the vector flow outwards from a point is equivalent to the volume charge density, ρv. That is, if a single point particle is positively charged, then the electric field – since the electric flux density is proportional to the electric field – must flow outwards from that point. Consequently, this means that like charges must repel and unlike charges must repel.
Maxwell’s second equation, Gauss’s Law for Magnetic Fields, is similar to the first except that the divergence of the magnetic flux density is zero, rather than the (non-existent) magnetic volume charge density. Experimental data has showed no evidence of magnetic charges, even today in modern physics. This means that the magnetic field lines cannot all be diverging or converging from a point; they must form a closed loop. Gauss’s Law for Magnetic Fields implies that magnetic monopoles (charges) do not exist, but rather, the basic entity for magnetism must be the magnetic dipole.
The third equation, Faraday’s Law, states that the curl of the electric field is equivalent to the negative rate of change of the magnetic flux density with respect to time. Since the magnetic flux density is proportional to the electric field, this means that a time-changing magnetic field will result in an direction-dependent electric field around it and vice versa.
The fourth equation, Ampere’s Law, can be explained by looking at Ampere’s original equation, ∇xH=j. Ampere’s original equation states the electric charge density is equal to the curl of the magnetic field, ie: a current flowing through a wire will result in a direction-dependent magnetic field circling the wire. This is true, however, Maxwell noticed that a circling magnetic field would form even with no conduction path, ex: through a simple capacitor. Ampere’s original equation did not predict this. Maxwell corrected Ampere’s original equation to describe the electric field created caused by a change in electric flux density...