Maxwell third equation and its derivation

Statement

(a) It states that,whenever magnetic flux linked with a circuit changes then induced electromotive force (emf) is set up in the circuit. This induced emf lasts so long as the change in magnetic flux continues.

(b) The magnitude of induced emf is equal to the rate of change of magnetic flux linked with the circuit.

Therefore induced emf= – dφm/dt

Where φm=∫B.dS (5)

Here negative sign is because of Lenz’s law which states that the induced emf set up a current in such a direction that the magnetic effect produced by it opposes the cause producing it.

Also definition of emf states that emf is the closed line integral of the non-conservative electric field generated by the battery.

That is emf=∫E.dL (6)

Comparing equations (5) and (6), we get

∫E.dL= – ∫s d/d t B.dS (7)

Equation (7) is the integral form of Maxwell’s third Equation or Faraday’s law of electromagnetic induction.