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Students in an introductory physics lab are performing an experiment with a parallel-plate capacitor made of two circular aluminum plates, each 20 cm in diameter, separated by 1.0 cm. How much charge can be added to each of the plates before a spark jumps between the two plates? For such flat electrodes, the field that causes a spark is at the high end of the range pre- sented in the chapter; assume a value of 3 * 106 N/C.

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Answer:

Q = 0.83 μC

Explanation:

  • Assuming that plates are much larger than the distance between them, we can think the electric field as constant and perpendicular to the outer surface of the plates.
  • Applying Gauss' law to a rectangular surface half inside one of the plates and half outside it, since E and A are parallel each other, and E is zero on the other three faces, we can find the following expression for the electric field created by the charge on the plate:

      [tex]E = \frac{Q*A}{\epsilon_{0} } (1)[/tex]

  • Solving for Q, replacing E by the maximum electric field that doesn't cause the dielectric strength to break (3*10⁶ N/C), we get:

      [tex]Q_{max} = E_{max} * \pi *\frac{d^{2}}{4} *\epsilon_{0} = 3e6N/C*\pi *\frac{(0.2m)^{2} }{4} * 8.85e-12C2/Nm2 = 0.83\mu C (2)[/tex]

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