State Faraday’s laws of electromagnetic induction. Express it mathematically.
Answers
Faraday's law states that the absolute value or magnitude of the circulation of the electric field E around a closed loop is equal to the rate of change of the magnetic flux through the area enclosed by the loop. The equation below expresses Faraday's law in mathematical form.
ΔΦB/∆t (through a fixed area) = -Σaround loop E∙∆r (at a fixed time)
The minus sign in this equation tells us about the direction of the circulation. (See below.)
When the magnetic flux through the area enclosed by the loop changes, Σaround loop E∙∆r is not zero, the electric field E circulates.
E∙∆r is the work done per unit charge by the electric field in moving the charge a distance ∆r.
If the loop is an actual wire loop, then there is actual work done by the induced field on free charges.
Σaround loop E∙∆r is the work per unit charge by the field in moving the charge once around the loop.
This is an induced emf, and it is measured in Volts.
The induced emf causes a current to flow without a potential difference due to separated charges.
ΔΦB/∆t (through a fixed area) = induced emf
The induced electric field is NOT a conservative field. When you move a charge against the induced field once around the loop, you have to do work. But your work is NOT stored as potential energy. You cannot let the electric field do work to recover the energy you expended in moving the charge. The induced electric field disappears as soon as the magnetic flux is no longer changing. The work you do on a charge against the induced field is not locally stored. The energy may be transported away in the form of an electromagnetic wave. Electromagnetic waves carry energy through free space.
Faraday's laws of electromagnetic induction.
(a) First law : Whenever there is a change in the magnetic flux associated with a circuit, an e.m.f. is induced in the circuit.
(b) Second law : The magnitude of the induced e.m.f. is directly proportional to the time rate of change of magnetic flux through the circuit.