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Problem 26.12: Calculate capacitance of concentric spheres

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The animation shows a spherical conductor surrounded by a conducting spherical shell. The two conductors have equal but opposite charge and the voltage difference between the two is 50 V (position is given in centimeters and charge is given in nanocoulombs). The field vectors for the electric field (kQ/r2) are shown in the region between the shell and the inner sphere and are zero everywhere else. Restart.

  1. Develop an expression for the charge as a function of the radius of the outer sphere and verify it with the animation.
  2. Develop an expression for the capacitance as a function of radius.
  3. Does the capacitance increase or decrease with increasing shell size? Explain.

Problem authored by Anne J. Cox.

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