Determine the rate at which the electric field changes between the round plates of a capacitor, 8.0 cm in diameter, if the plates are spaced 1.5 mm apart and the voltage across them is changing at a rate of 140 V/s .

Respuesta :

Explanation:

It is known that the relation between electric field and potential difference between the plates of a parallel plate capacitor is as follows.

           E = [tex]\frac{V}{D}[/tex]

So, differentiating this on both the sides with respect o time as follows.

            [tex]\frac{dE}{dt} = \frac{1}{D} \frac{dV}{dt}[/tex]

Hence, rate of electric field changes between the plates of parallel plate capacitor as follows.

            [tex]\frac{dE}{dt} = \frac{1}{D} \frac{dV}{dt}[/tex]

                 = [tex]\frac{1}{1.5 \times 10^{-3} m} \times 140 V/s[/tex]

                 = [tex]93.33 \times 10^{3}[/tex] V/ms

Thus, we can conclude that the rate at which the electric field changes between the round plates of a capacitor is [tex]93.33 \times 10^{3}[/tex] V/ms.