Electromagnetic Induction - ASKnLearn

Dunman High School (Senior High Physics Department)A3Maxwell’s Equations (Enrichment only)Maxwell's equations are a set of four equations that form thefoundation of classical electrodynamics, classical optics, andelectric circuits. These fields in turn underlie modern electricaland communications technologies. Maxwell's equations arenamed after the Scottish physicist and mathematician JamesClerk Maxwell. Maxwell's equations demonstrate that electricity,magnetism and light are all manifestations of the samephenomenon, namely the electromagnetic field. Subsequently, allother classic laws or equations of these disciplines becamesimplified cases of Maxwell's equations. For example, equationssuch as P=IV and n=sin i / sin r can be derived from these set ofequations. Maxwell's achievements concerning electromagnetismhave been called the "second great unification in physics", afterthe first one realised by Isaac Newton.Maxwell’s Equations∮ E. dd = q ε 0– Gauss’ Law for electricity (used to derive Coulomb’s Law)∮ B. dd = 0 – Gauss’ Law for magnetism∮ E. ds = − dΦ BdtdΦ∮ B. ds = μ 0 I + μ 0 ε E0dtExplanation of the equations– Faraday’s Law of induction– Ampère's circuital law with Maxwell’s correction∮ E. dd = q ε 0∮ E. dd is the total electric field through a closed surface area is equivalent to the amount ofcharge q enclosed within the closed surface area over the permittivity of free space. This is usedto derived Coulomb’s law as the surface area of a sphere is 4πr 2 so the relationship yieldsE × 4πr 2 qq= or E =ε 04πε 0 r 2 B. dd = 0This expression states that the total magnetic field through a closed surface area is always equalto zero. The consequence of this equation is that unlike electric charges which can exist as asingle positive or negative charge, ‘magnet monopoles’ do not exist. A magnet must come in bothnorth and south pole so the field lines must go from a north pole and end at a south pole. E. ds = − dΦ BdtThis is the equation for Faraday’s law discussed in this chapter. Recall from E-field that ∫ E. ds = V,hence the e.m.f. across a closed path is given by the expression above. B. ds = μ 0 I + μ 0 ε 0dΦ EdtAmpere’s Law states that the magnetic field across a closed path depends on the amount ofcurrent I passing through the closed loop. Hence for an infinitely long straight wire, a closed circleoutside the wire gives 2πr × B = µ 0 I or B = µ 0 I/2πr (see Topic 15 on EM). However, Maxwell’scorrection states that a changing electric flux linkage will also produce a magnetic flux.9646 Physics (2012)Topic 16: Electromagnetic Induction 16-17