Each plate of a parallel‑plate capacitor is a square of side 0.0479 m, and the plates are separated by 0.479 × 10 − 3 m. The capacitor is charged and stores 8.11 × 10 − 9 J of energy. Find the electric field strength E inside the capacitor.

Respuesta :

Explanation:

It is known that the relation between electric field and potential is as follows.

             E = [tex]\frac{V}{d}[/tex]

And, formula to calculate the capacitance is as follows.

           C = [tex]\frac{\epsilon_{o} A}{d}[/tex]

              = [tex]\frac{8.854 \times 10^{-12} \times (0.479 m)^{2}}{0.479 \times 10^{-3}}[/tex]

              = [tex]4.24 \times 10^{-9}[/tex] F

Hence, energy stored in a capacitor is as follows.

         W = [tex]\frac{1}{2}CV^{2}[/tex]

          V = [tex]\sqrt{\frac{2W}{C}}[/tex]

        E = [tex]\sqrt{\frac{2W}{d^{2}C}}[/tex]

            = [tex]\frac{2 \times 8.11 \times 10^{-9} J}{(0.479 \times 10^{-3})^{2} \times 4.24 \times 10^{-9}}[/tex]

            = [tex]16.687 \times 10^{3} N/C[/tex]

Thus, we can conclude that electric field strength E inside the capacitor is [tex]16.687 \times 10^{3} N/C[/tex].