7. (3 points) Electrical quadrupole consists of four alternating charges (+Q or

Question

7. (3 points) Electrical quadrupole consists of four alternating charges (+Q or -Q) at the corners of a square as shown in the Figure to the right. The distance between adjacent charges is 2a. The origin is located in the center of the square as shown. +Q Charges are positioned in free space (a) In which direction will the electric field produced by the quadrupole point at observation points on x- 2a axis with x 0? Use unit vectors of x-y coordinate system depicted and don't forget to specify sign! +Q (b) Write an expression for the electric field E(x) (a vector produced by the quadrupole for observation points on x-axis. Use Q, a, x, Eo, and anything else you may need. (c) Now assume x-coordinate of observation points on x-axis is much larger than a. Simplify the expression obtained in part (c) assuming x> a. Hint: the following expansion may be useful T 1- where is a number or an expression which is much smaller than x

Explanation / Answer

in the question of part c there they mentioned x>>a and also mentioned in the note that if x>0 the first term is greater that second term and the point E-field will be alone +y axis only. so he neglected the a2 and he solved only for the (x-a)2 and (x+a)2.

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