# A 10 cm-long uniform line of charge has a linear charge density of = 1000 C/m. The line lies along the x-axis and its left edge is at the origin.

A 10 cm-long uniform line of charge has a linear charge density of λ = 1000 μC/m. The line lies along the x-axis and its left edge is at the origin. Derive a formula for the electric field as a function of position along the x-axis for x > 0.1 m (y = z = 0).(a) For r >>> 0.1 m, the field will look like that of a point charge with a charge of μC.Now let’s calculate the field strength closer in – at 0.28 m (y = z = 0).(b) We can get an estimate of the magnitude of the field by assuming all the charge is at the center of the line (instead of it being uniform distributed). What is this estimate of the magnitude of the field? N/C(c) We can get a lower limit of the magnitude of the field by assuming all the charge is at the left edge of the line (instead of it being uniform). What is this lower limit of the magnitude of the field? N/C(d) We can get an upper limit of the magnitude of the field by assuming all the charge is at the right edge of the line (instead of it being uniform). What is this upper limit of the magnitude of the field? N/C(e) Now do the full exact calculation. What is Ex at the position (0.28 m, 0, 0)? (For this answer, also include the sign to indicate direction of the field.)Ex = N/CNote: the graders will be looking closely at this problem, so be sure to have a detailed and carefully explained solution to this problem – particularly setting up the integral to get the exact expression for the electric field. The integral is a simple one (just that of xn) but you will probably need to use a substitution like x’ = x – a to get it into the simplest form to integrate. Be sure to simplify your final expression using algebra.

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