Consider two thin rods of charge with linear charge densities + and - located at

Question

Consider two thin rods of charge with linear charge densities + and - located at x = -a and x = +a on the x-axis and perpendicular to the plane of the black paper. Again, let point A be the origin, B be on the x-axis at x = -a/2, C be on the x-axis at x = +a/2, D be on the y-axis at y = +a/2, and E be on the y-axis at y = -a/2. Use the expression for the electric field of a infinite line charge (it is different than for point charges) to determine the algebraic expressions in terms of (k, , a) for the net electric field magnitude at points A, B, C, D, and E. (In cases D and E you will have to sum two vector components to get the net horizontal E-field.) Using your algebraic expressions evaluate numerically the following theoretical ratios. Show all work on how you came to your final expression (k, , a should cancel leaving you with a number):

EB/EA =
EC/EA =
ED/EA =
EE/EA =

Explanation / Answer

electric field due to infinite electric line charge at a perpendicular distance r from the line is given by

E = /(2r) . let 1/2 =k then E = k/r

electric field at A, D,E will be same because on the same line at a distance a from the lines

EA,D,E = 2k/a in the +x direction ( 2 comes because of the 2 lines of charges and forces being in the same direction)

electric field at B and C will be same

EB,C = force due to one line charge + force due to the other line charge

= k/(a/2) +k/(3a/2) = 8k/3a

EB/EA = 4/3
EC/EA = 4/3
ED/EA = 1
EE/EA = 1

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