It is not possible to have an electric field line be a closed loop. Explain why

Question

It is not possible to have an electric field line be a closed loop. Explain why this is true using potential and equipotential lines. 1. 2, An infinite cylinder with radius R with a uniform charge density is centered on the z-axis. Give the potential in all space. Plot the potential as a function of the distance from the z-axis a. b. Hints for problem 2: i. The potential should be continuous function. Match the potential at the ii. You may (and should) use previous discussions on the electric field from an i Your answer may not make physical sense as the distance goes to infinity. edge of the cylinder infinite cylinder that we discussed last week during Gauss' law lectures. Think about why this might be

Explanation / Answer

1) Equipotential lines are the lines along which the potential is constant. When we draw electric field lines with equipotential lines, we observe that electric field lines cut the equipotential lines at exactly 90 degree at all points. It means no two electric field lines will cross.

Also, electric lines of force originate from a positive charge and terminate at a negative charge.Thus, if we consider that a single line of force emerges out of a positive charge and loops back to the same point from where it originated, it would mean that there are two same charges placed exactly at a same point, which is non-sensical.

2)

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