(a) 0
The magnetic field strength insidea a parallel-plate capacitor with changing electric field can be found by applying Ampere's law:
(1)
where
is the circumference of the circular line of radius r with axis coincident to the axis of the capacitor, used to calculate the magnetic field
B is the strength of the magnetic field
is the displacement current enclosed by the area of the circular line mentioned above, and it is equal to
(2)
where
is the rate of change of electric flux through the area enclosed by the line
is the rate of change of the electric field
Rewriting eq.(1), we find
which is valid for r < R (where R=5.0 cm is the radius of the plates of the capacitor).
In this part of the problem,
r = 0
since we are on the axis; so substituting r=0 inside the formula above, we find
B(0) = 0
(b)
In this part, we have
r = 3.0 cm = 0.03 m
The formula used in part (a) is still valid since r<R, so we can directly use it to find the magnitude of the magnetic field:
(c)
In this part, we have
r = 7.0 cm = 0.07 m
so here
r > R
therefore we need to substitute with in eq. (2), since the area through which the flux is calculated is only (there is no electric field outside the area of the capacitor). So we find
and therefore