PLEASE SHOW YOUR WORK!!! IM CONFUSED. Line charges: another algebraic problem Co

Question

PLEASE SHOW YOUR WORK!!! IM CONFUSED.

Line charges: another algebraic problem Consider two thin rods of charge with linear charge densities +Lambda and -Lambda located at x = -a and x = +a on the x-axis and perpendicular to the plane of the black paper (i.e. into and out of the board). 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 an infinite line charge (it is different than for point charges) to determine the algebraic expressions in terms of (k, Lambda, 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 (k, Lambda, 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 = ?/(2?r?) . 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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