Question

Consider the following charge distribution:

The charge density of the segment of the line extending from zo + R to 3R is \lambda_{1}=\alpha(x-a)+\lambda_{0} the charge density of the arc is \lambda_{2}=\lambda_{0} \cos \left(\frac{\theta}{3}\right) and the charge density of the segment extending from oR to -3R is \lambda_{3}=\beta\left(x^{2}-b\right)+\frac{\lambda_{0}}{2} where a, ß, a, and b are constants. (The constants a and b ensure no discontinuities in the-charge distribution. They may be found in terms of zo and R, but you are not required to doso.) Find the electric potential at the position zo.

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