Consider two infinite uniform straight line$-$charges each with constant

positive linear charge density $(=$dq$/$dL$),$ both at rest in the lab frame S$.$ The line

charges are parallel to each other with a separation d between them. See figure.

In the following questions, you need to determine the electric and$/$or magnetic forces

on a charge segment LAB of one of the line charges. Support your answer with

arguments of physics laws. A direct quotation of line charge formulas without

arguments will not earn full credit.

a$)(5$ points$)$ What is the electric force FE on charge segment LAB $($in the ref.

frame S$)?$

b$)(5$ points$)$ What is the magnetic force FB on LAB $($again$,$ in S$)?$

Now, in reference frame S$$ that is moving in velocity V parallel to the line$-$

charge. Both the line$-$charges and q$0$ are moving at velocity V$.$

c$)(5$ points$)$ What is the electric force on LAB F$$E in S$?($You may modify

from your answer in a$)$ above without repeat the derivation procedure$).$

d$)(10$ points$)$ What is the magnetic field at the position of LAB as seen in S$?$

e$)(5$ points$)$ What is the magnetic force F$$B on LAB in S$?$

f$)(5$ points$)$ What is the combined electric and magnetic forces F$$EM on LAB

as seen in S$?$

g$)(5$ points$)$ What is the ratio between the combined electric and magnetic

forces seen in S and S$.($i$.$e$.$ FEM:F$$EM$).$ Express your answer in terms of

Lorentz boost factor only.