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). Charge Distribution 3 Largest (most positive) Electric Field Charge Distribution 1 Second Largest Electric Field Charge Distribution 5 Middle Electric Field Charge Distribution 4 Second Smallest Electric Field Charge Distribution 2 Smallest (most negative) Electric Field

Explanation / Answer

formula for Electric field E = KQ/r^2

so in fig 1.

Enet = KQ/(d/2)^2 + K2Q/(d/2)^2

Enet = 4 KQ/d^2 + 8KQ/d^2 = 12 KQ/d^2

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in fig 2:

Enet = (KQ/d^2 - 2KQ/d^2) = -KQ/d^2

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in fig 3:

Enet = -4KQ/d^2 - 12KQ/d^2 = -16 KQ/d^2

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in fig 4:

Enet = (-2KQ/d^2 - 2KQ/d^2) = - 4KQ/d^2

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in fig 5:

Enet = (4KQ/d^2 - 4KQ/d^2) = 0

since positive is highest,

fig 1 > fig 5 > fig 2 > fig 4 > fig 3

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