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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