The figure below shows arrangements of three fixed charges. In each situation, a

Question

The figure below shows arrangements of three fixed charges. In each situation, a point P is also identified. All of the charges are the same size, q, but they can be either positive or negative as indicated. The charges and point P all lie along a straight line. The distances between adjacent items, either between two charges or between a charge and point P, are all the same. There are no other charges in this region Rank these situations from largest to smallest on the basis of the magnitude of the electric field at point P. The direction of the electric field is not important. Ties are possible. Use the symbols > and = to indicate your ranking, listing any that are equal in alphabetical order. For example, if Y and Z are the same and are both greater than X, then you would enter Y-Z>X (note: Z-Y>X would be incorrect, since Y and Z, being equal, must be in alphabetical order) LARGEST E-FIELD SMALLEST E-FIELD

Explanation / Answer

for A)

E = kq (1/a2 + 1/(2a)2 + 1/(3a)2) = (1.4)kq/a2

for B)

E = kq (- 1/a2 + 1/(2a)2 - 1/(a)2) = (- 1.8)kq/a2

for C)

E = kq (-1/a2 + 1/(2a)2 + 1/(3a)2) = (- 0.64)kq/a2

for D)

E = kq (-1/a2 + 1/(a)2 + 1/(2a)2) = (0.25)kq/a2

for E)

E =  kq (1/a2 + 1/(a)2 + 1/(2a)2) = (2.25)kq/a2

for F)

E = kq (1/a2 - 1/(2a)2 + 1/(3a)2) = (0.86)kq/a2

E>B>A>F>C>D

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