Question

Suppose that a parallel-plate capacitor has circular plates with radius R = 18 mm and a plate separation of 3.6 mm. suppose also that a sinusoidal potential difference with a maximum value of 153 V and a frequency of 60 Hz is applied across the plates: that is, V = (153 V) sin[2 ?(60 Hz)t] Find Bmax, the maximum value of the induced magnetic that occurs at r = R.

Answer 1

Given:

is the radius of the circular plate

is the separation distance of the circular plates

is the voltage applied across the plates with maximum voltage as 153 V and frequency as 60 Hz.

we will use vacuum as the medium (dielectric missing) so the permittivity is

Capacitance is given by

..............EQ1

The current in the circuit is given by:

The maximum current is

The induced magnetic field at a distance 'r' is given by:

Substituting and from EQ1

We know and , substituting all constants and variables we get;