In this problem we consider two charges placed on the y-axis and calculate the r

Question

In this problem we consider two charges placed on the y-axis and calculate the resulting potential for points on the y-axis. A positive charge, +q, is placed at the point (0,-a) and a negative charge, -q, is placed at the point (0,a).

a) Make a sketch showing the position of each of the charges. Be sure to included labeled axes.

b) Find an expression for the potential, V, for all points on the y-axis as a function of y. Take V to be zero at infinity.

c) Graph V for points on the y-axis as a function of y from y=-2a to y=2a.

d) How do the answers to parts b and d change if the position of the charges is interchanged so that the positive charge is at (0,a) and the negative charge is at (0,-a)?

Explanation / Answer

a)

b)

V = kq (1/(|y+a|) - 1/(|y-a|))

c)

d)

potential will be: V = kq (1/(|y-a|) - 1/(|y+a|))

and plot:

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