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A circular parallel-plate capacitor with a spacing of 1.6 mm is charged to produce a uniform electric field with a strength of 2.7 × 106 N/C. What plate radius is required if the stored charge is −1.07 µC? The permittivity of a vacuum is 8.8542 × 10−12 C2/N · m2. Answer in units of m.

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usmanbiu

Answer:

    r = 0.119 m

Explanation:

distance (d) = 1.6 mm = 0.0016 m

electric field strength (E) = 2.7 x 10^{6} N/C

charge (Q) = -1.07 μC = -1.07 x 10^{-6} C

permitivity of vacuum = 8.8542 x 10^{-12} C^{2}/N

find the radius of the plate required

  • lets first find the voltage

        voltage (V) = E x d

        voltage (V) =  2.7 x 10^{6} x 0.0016 = 4320 V

  • lets also find capacitance (C) = Q/V

        C =  -1.07 x 10^{-6} / 4320 = 2.47 x 10^{-10} F

  • the value of capacitance (C)  is also = E₀A / d

        we can rearrange the equation above to have our area (A) = Cd/ E₀

         A = [tex]\frac{2.47 x 10^{-10} x 0.0016}{8.8542 x 10^{-12}}[/tex]

         A = 0.0446 m^{2}

  • Area (A) = π x [tex]r^{2}[/tex]

       r = [tex]\sqrt{\frac{a}{π} }[/tex]

       r = [tex]\sqrt{\frac{0.0446}{π} }[/tex]

      r = 0.119 m

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