Maxwell made a modification to Ampère's law to include an additional term to complete the relation of the B field to the E field. The full Ampère's law is according to Maxwell: & B di = (Ic + Io) (eq. 1)
Using Stokes' theorem for a general arbitrary surface S and the definition of current being the surface integral of the current density to arrive at the differential form of the full Ampère's law; i. e. show that: Prove this
D x B = (Jc + Jo)
R-equation from (eq. m (eg. 10}
Next derive an explicit expression for the displacement current density T You can do so by first considering Gauss' law density J. You can do so by first considering Gauss' law
(i) Eo ff. È. dś = Qo
Qo is the displacement current. Take the partial time derivative of this expression to get the displacement current Io, then recall how this relates to the current density to give an expression of the displacement current density in terms of what is known as the electric displacement field defined as
Ď = Eo E)
with this explicit form of the displacement current density tell me what the curl of the magnetic field equals in terms of Mo, Jc and Ď.
(ii) D x B = ?