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8. Positive charge is distributed along a very thin wire of length L, centered at the origin of an x-axis. The linear density obeys the following relationship, u(x)-olr, where 14, and β are constants (a) Derive an expression for the electric field vector on the y-axis generated by this charge distribution. (b) How does this expression change, if the wire is infinitely extended? How does the expression derived at (a) change, if β-0, and what does β-O mean physically? (c) What is the total amount of charge on the wire of finite length L?

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