Question
The following questions refer to the figure below.
[show the details of your calculations; put a box around each final answer .] Consider an infinitely-long continuous distribution of charge which lies along the x-axis extending from x0 to positive infinity. The line carries a position-dependent charge per unit length lambda(x) = lambda 0 The constants x0 and lambda 0 have dimensions of length and charge-per-length, respectively. These were used to make the dimensions work out conveniently, that is, you can easily check your answers with dimensional analysis. Write down the general expression for how to calculate the total charge, then evaluate the integral. (Your answer should have the correct dimensions: that is some number times lambda 0 x0.) Write down the general expression for how to calculate the potential at the origin (point P), then evaluate the integral.
Explanation / Answer
Am representing lambda and lambda0 by l and l0 for convenience.
(a) Total charge is integral of l*dx
= int l0x0^2 / x^2 dx
l0x0^2 (-1/2x), x= x0 to infinity
= l0x0/2
