Suppose that a circular-plate capacitor has a radius R of 32.1 mm and a plate separation of 4.80 mm. A sinusoidal potential difference with a maximum value of 162 V and a frequency of 60.0 Hz is applied between the plates. We have to find the maximum value of the induced magnetic field at .

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From the data of the problem we note that the potential can be described by the function

In a parallel-plate capacitor with plate separation d, the electric field E and the potential difference V are related as

,

we have

We note that

Ampere’s law is

Applying it to an Amperian loop of radius , we have

The maximum value of the magnetic field between the plates at will therefore be