Maxwell’s modified form of Ampere’s circuital law is:

Answer (Detailed Solution Below)

Option 4 :
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CONCEPT:

  • Amperes law: The line integral of the magnetic field around any closed curve is equal to μo times the net current I threading through the area enclosed by the curve.

Ampere’s law in this form is not valid if the electric field at the surface varies with time.

  • Displacement current (ID): It is that current that comes into existence, in addition to the conduction current, whenever the electric field and hence the electric flux changes with time.

EXPLANATION:

  • To modify Ampere’s law, Maxwell followed a symmetry consideration.
  • By Faraday’s law, a changing magnetic field induces an electric field, hence a changing electric field must induce a magnetic field. As currents are the usual sources of the magnetic field, a changing electric field must be associated with the current. Maxwell called that current as displacement current.
  • To maintain the dimensional consistency, the displacement current is added in ampere’s law

Where,  is the displacement current. So option 4 is correct.

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