|
549. Problem 40.14 (RHK) A capacitor consisting of two circular plates with radius
|
is
connected to a source of emf
,
where
and
. The
maximum value of the displacement current is
.
Neglecting fringing of the electric field at the edges of the plates,
we have to find the maximum value of the current
;
the maximum value of
,
where
is
the electric flux through the region between the plates; the separation
between the plates d; and the maximum value of the magnitude of
between the plates at a distance
from
the centre.
|
Solution: Click For PDF Version From the data of the problem we note that the emf applied across the plates of the capacitor can be described by the function
Let the separation between the plates be
The displacement current
The maximum value of
It is given that
Therefore,
The maximum value of the charging current will be equal to the maximum value
of the displacement current. Therefore, the maximum value of the charging
current will be
We will next calculate the separation between the plates. We know that
Therefore,
We will find next the maximum value of
Considering an Amperian circular loop of radius
|
.
.
Variation of the electric field between the plates will be given by the function
is given
in terms of the change of electric flux per unit time by the relation
.
.
