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Exploration 24.4: Application of Gauss's Law

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A point charge has radial (spherical) symmetry about the center of the charge, while a line charge has cylindrical symmetry about the center of the wire (position is given in meters and electric field strength is given in newtons/coulonb). However, a two-dimensional view of both can look the same. Restart.

Consider the two configurations. One is a point charge and one is a line of charge (pointing into and out of the screen). Which is which? The electric field is different for the two cases (and you use two different Gaussian surfaces).

  1. As a function of the distance away from the charge (as a function of r), what is the electric field of a point charge?
  2. Therefore, if you measure the electric field at some point and then measure it twice as far away, how much should the electric field be decreased?
  3. Which configuration, then, is a point charge?
  4. Use Gauss's law to find an analytic expression for the electric field around a line of charge. You may find the following diagram useful:

  1. If you measure the electric field at some point and then move twice as far away, how should the field drop off from a line of charge?
  2. Does the electric field of the other configuration agree with this?

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Exploration authored by Anne J. Cox.
Script authored by Wolfgang Christian.

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