A square consists of four positively charged rods, each of length l and charge Q

Question

A square consists of four positively charged rods, each of length l and charge Q. On each rod, the charge is uniformly distributed. In this problem, neglect gravity.

(a) How much work would it take to move a small particle of charge +q to the

center of the square if the particle starts very far away from the square?

(b) About how much work would it take to move a small particle of charge +q to a

point a distance 100l away from the center of the square (on an axis perpendicular to the plane of the square), if the particle starts very far away?

Explanation / Answer

a)

potential due to one side at center

V=2kQln(L/2)

potential due to all the four sides at center=V1=8kQlnL

potential at 100 m=V2=4kQln((L/2)2+1002)

potential at infiinity=V3=0

a)

W=(V3-V1)q=-V1q

b)

W=(V3-V2)q=-V2q

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