Using Gauss\'s law, calculate the electric field in the plane of the page at a p

Question

Using Gauss's law, calculate the electric field in the plane of the page at a point r > R from the center of the charge distribution Q. Figure 2: A charge Q radiating an electric field A in 2- D - the electric field is confined to the plane of the page. The dashed line indicates a loop P that encloses the charge. The vector ds represents a small patch of the perimeter. In Problem 1, you showed that The electric field for a point charge radiating in 3-dimensions has a distance dependence of 1/r^2. In Problem 2 you showed that the electric field for a point charge radiating in 2-dimensions has a distance dependence of 1/r. Consider again the 2-dimensional case described in Problem 2. What distance dependence do you expect for the electric potential? Justify your answer.

Explanation / Answer

electric potential V=-kQ/r

so potential depends on 1/r

potential is the amount of work done.=forceX displacement

force depends on 1/r2X r=1/r

hence potential depends on 1/r

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