Q. 1

Show that the dimensions of the displacement current are that of an electric current.

Answer :

The displacement current Id is produced by a varying electric


field. It is given by the relation



where ϵ0 is the electric permittivity of free space(vacuum) and is


equal to 8.85 × 10-12 C2 N-1 m-2 and ϕE is the electric flux produced


by the time varying electric field.


To find the dimension of Id and check whether it is the same as that


of electric current, we need to find the dimension of .


We can simplify using Gauss’s Law. According to Gauss’s law


the electric flux ϕE through a surface is given as



Using the above relation, the displacement current becomes




The dimension of displacement current is the dimension of the


quantity in the R.H.S of the above equation



As [A] is the dimension of electric current so displacement current


has same dimension as that of electric current.


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