State explain Faraday's laws of electromagnetic induction. Give their mathematical form.

Explanation

Faraday.s laws of electromagnetic induction: See Short Answer Type Question No. 4 (2 Marks) Mathematical explanation:
If `ph_(1)` is the amount of magnetic flux linked with coil at time `t_(1) and phi_(2)` is the magnetic flux linked with coil at time `t_(2)` then
Rate of change of magnetic flux `=(ph_(2)-ph_(1))/(t_(2)-t_(1))`
Therefore, according to Faraday.s second law, the magnitude of induced emfis directly proportional to the rate of change of magnetic flux
i.e., `e prop ((ph_(2)-phi_(1)))/((t_(2)-t_(1)))" or "e=(-k(phi_(2)-phi_(1)))/((t_(2)-t_(1)))`
or `e=(-k d phi)/(dt)`
or `e=(-k d phi)/(dt)`
where `d phi` is smal change in magnetic flux occurred in small time dt, k is constant of proportionality and its value in SI units comes out to be 1 and -ve sign shows, that induced emf always opposes the change in magnetic flux.
`therefore e=-(d phi)/(dt)`
The above cqn. is mathematical representation of Faraday.s law of EML If coil is made of Nturns, then `e=-N (d phi_(B))/(dt)`
which is commonly known as Faraday Lenz.s law.