A closed loop of magnetic field is produced by a changing electric field. Are electric field and time varing electric fiels necessarily non zero at all points on tte loop and in the area enclosed by the loop?

Asked by Himanshukesarwani97 | 20th Jan, 2020, 10:22: PM

Expert Answer:

Maxwell's equation of Ampere's law is written as
begin mathsize 14px style nabla cross times B space equals space mu subscript o J space plus space mu subscript o epsilon subscript o fraction numerator partial differential E over denominator partial differential t end fraction end style
where B is magnetic field induction, J is current density in the region of magnetic field, E is electric field , 
μo and εo are respectively permeability and permissivity of medium.
 
Second term in the right hand side is due to displacement current.
 
In integral form, above equation is written as, begin mathsize 14px style contour integral B. d l space equals space mu subscript o I subscript e n c end subscript space plus space mu subscript o epsilon subscript o integral fraction numerator partial differential E over denominator partial differential t end fraction times d A end style
Hence it can be inferred  from above integral equation, closed loop magnetic field is produced by
enclosed current of the loop and displacement current produced in the loop area due to change in electric field.
 
In the absence of enclosed current, closed loop magnetic field is produced only by time varying electric field
in the area enclosed by the loop

Answered by Thiyagarajan K | 22nd Jan, 2020, 08:46: AM

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