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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).
- As a function of the distance away from the charge (as a function of r), what is the electric field of a point charge?
- 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?
- Which configuration, then, is a point charge?
- 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:
- 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?
- Does the electric field of the other configuration agree with this?
Exploration authored by Anne J. Cox.
Script authored by Wolfgang Christian.