(2) Imagine we have a semi-infinite line of charge with uniform charge density s

Question

(2) Imagine we have a semi-infinite line of charge with uniform charge density situated on the z-axis. Semi-infinite means that it starts at z = -infinity and ends at a point z = L. We want to calculate the electric field at a point, P, located at (x, 0, L)

(a) What is the best choice for the shape of the tiny pieces of charge?

(b) Find an expression for the charge of one of these pieces dq in terms of parameters given.

(c) What is the distance between any little piece of charge and the point P?

(d) What is the ˆr vector in terms of given parameters?

(e) Using symmetry, discuss what components of the electric field will be zero (if any). If no components are zero, explain why not

Explanation / Answer

i.e. Q = ne

where , e = 1.6 * 10-19 C

If we consider the small pieces of line elements then the best shape is small cylinder of length dL.

So, dq =.dL

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