- Maxwell proposed that the time varying electric field can generate magnetic field.
- Time varying magnetic field generates electric field (Faraday-Lenz law).
- According to Faraday Lenz law an emf is induced in the circuit whenever the amount of magnetic flux linked with a circuit changes.
- As a result electric current gets generated in the circuit which has an electric field associated with it.
- According to Maxwell if Faraday’s law is true then the vice-versa should also be true, i.e. a time varying electric field should also be able to generate amagnetic field.
- According to Ampere’s Circuital law, the line integral of magnetic field over the length element is equal to μ0 times the total current passing through the surface ∫dl = μ0 l
- According to Maxwell there was some inconsistency in the Ampere’s circuital law.
- This means Ampere’s circuital law was correct for some cases but not correct for some.
- Maxwell took different scenarios i.e. he took a capacitor and tried to calculate magnetic field at a specific point in a piece of a capacitor.
- Point P as shown in the figure is where he determined the value of B, assuming some current I is flowing through the circuit.
- He considered 3 different amperial loops as shown in the figs.
- Ampere’s circuital law should be same for all the 3 setups.
Case 1: Considered a surface of radius r & dl is the circumference of the surface, then from Ampere’s circuital law
∫ B.dl = μ0 l
or B(2πr) = μ0 l
or B = μ0 l / 2πr
Case 2 : Considering a surface like a box & its lid is open and applying the Ampere’s circuital law
∫ B.dl = μ0 l
As there is no current flowing inside the capacitr, therefore I = 0
Or ∫ B.dl = 0
Case 3: Considering the surface between 2 plates of the capacitor, in this case also I=0, so B=0
- At the same point but with different amperial surfaces the value of magnetic field is not same.They are different for the same point.
- Maxwell suggested that there are some gaps in the Ampere’s circuital law.
- He corrected the Ampere’s circuital law. And he made Ampere’s circuital law consistent in all the scenarios.