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Problem 25.12: Cylindrical or spherical symmetry?

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The animation shows either concentric cylinders or concentric spheres (position is given in centimeters and electric potential is given in volts). Restart. You can move the test charge around to measure the electric potential. Develop an equation for the voltage as a function of position for concentric cylinders and concentric spheres. The electric field outside a charged sphere = kQ/r2. Outside a charged rod it is 2kλ/r, where k = 9 x 109 Nm2 and λ = charge/length.

  1. If this animation represented concentric spheres where the inner sphere has a voltage of 10 V and the outer sphere has a voltage of 0 V, how much charge would be on the center sphere? What, then, would be the equation for the voltage as a function of position between the spheres?
  2. If this animation represented concentric cylinders where the inner cylinder has a voltage of 10 V and the outer cylinder has a voltage of 0 V, what would the charge per unit length be on the inner cylinder? What, then, would be the equation for the voltage as a function of position between the cylinders?
  3. Does this animation represent concentric cylinders or concentric spheres?

Problem authored by Anne J. Cox.
Script authored by Mario Belloni, Wolfgang Christian and Anne J. Cox.

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