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Electric potential due to the presence of multiple charges

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A positive charge q1 is located to the left of a negative charge -q2. On a line passing through the two charges, there are two places where the total potential is zero. The first place is between the charges and is 4.00 cm to the left of the negative charge. The second place is 7.00 cm to the right of the negative charge.

a. What is the distance between the chares, d?
b. Find q1/q2, the ratio of the magnitude of the charges.

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In between:

k q1/(d-4) - k q2/4 = 0

k q1/(d-4) = k q2/4

d-4 = 4 q1/q2 -------------------- (1)

Potential to the right of charge -q2:

k q1/(d+7) - k q2/7 = 0

k q1/(d+7) = k q2/7

d+7 = 7 q1/q2 --------------------- (2)

From 1 and 2, (d-4) = 4 * (d+7)/7

7d - 28 = 4d + 28 è 3d = 56

d = 18.7 m

(b) (1)è q1/q2 = (d-4)/4 = 3.7

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