In 1929 M. R. Van Cauwenberghe succeeded in measuring directly, for the first time, the displacement current between the plates of a parallel plate capacitor to which an alternating potential difference was applied. He used circular plates whose effective radius was 40.0 cm and whose capacitance was 100 pF. The applied potential difference had a maximum value of 174 kV at a frequency of 50.0 Hz. (a) We have to calculate the maximum displacement current that was present between the plates. (b) We have to answer why the applied potential difference was chosen to be so high. (The delicacy of these measurements is such that they were only performed in a direct manner more than 60 years after Maxwell enunciated the concept of displacement current.)

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The displacement current is defined by the relation

where the flux due to the electric field between the plates of the capacitor of radius R is

.

Let d be the separation between the plates and let V be the potential difference between the plates. As the electric field between the plates is uniform, we have

The capacitance of a parallel plate (circular plates) capacitor is

.

Therefore,

,

and

In the experiment the potential difference varied simple harmonically with frequency and maximum value of 174 kV. We therefore have

Therefore, the maximum value of in the experiment was

In the experiment capacitance of the capacitor used was

Therefore, the maximum displacement current present in the experiment was

(b)

The displacement current is equal to product of the capacitance and the rate of change with time of the potential between the plates, and as the capacitance of the condenser was of the order of pico Farad, for the displacement current to be of the order of mA the potential difference had to be of the order of kV.