Five pairs of point charges are shown in the figure, labeled 1, 2, 3, 4, and 5.

Question

Five pairs of point charges are shown in the figure, labeled 1, 2, 3, 4, and 5. Rank these charge distributions in terms of the y-component of the electric field half-way between the charges.

Consider upwards positive, so that all upwards pointing fields are greater than all downwards pointing fields.

So, the most positive field (upwards) will be largest and the most negative field (downwards) will be smallest.

In the answer boxes below, the different charge distributions are listed in random order. Next to them are drop-down boxes with the answers 1 (most positive) to 5 (most negative).

Explanation / Answer

Here ,

for the electric field ,

E1 = - 2kQ/(d/2)^2 - k * Q/(d/2)^2

E1 = -12 k * Q/d^2

for the situation 2 ,

E2 = - 3kQ/(d)^2 - k * Q/(d)^2

E2 = -4 * k*Q/d^2

for region 3

E3 = kQ/(d/2)^2 + k * Q/(d/2)^2

E3 = 8 * k*Q/d^2

for 4

E4 = 2kQ/(d)^2 +2 k * Q/(d)^2

E4 = 4 * k*Q/d^2

for region 5

E5 = 0

Now , the electric field from the most positive to most negative

E3 > E4 > E5 > E2 > E1

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