# The two negative charges -q and -2q are at a distance of 20mm. The charges interact with

The two negative charges -q and -2q are at a distance of 20mm. The charges interact with a force of 1.8 x 10E-4H. How big is each charge?

Data: q1 – first charge (q1 = -q); q1 is the second charge (q1 = -2q); r – distance (r = 20 mm, in SI system r = 2 * 10 ^ -2 m); F – force of interaction (F = 1.8 * 10 ^ -4 N); for Wednesday we take air (vacuum).

Const: k – coeff. proportionality (k = 9 * 10 ^ 9 N * m2 / Kl)

1) Calculate the charge q: F = | q1 | * | q2 | * k / r ^ 2 = -q * -2q * k / r ^ 2 = 2q2 * k / r ^ 2, whence we express: q = √ (r ^ 2 * F / 2k).

Calculation: q = √ (r ^ 2 * F / 2k) = √ ((2 * 10 ^ -2) ^ 2 * 1.8 * 10 ^ -4 / (2 * 9 * 10 ^ 9)) = 2 * 10 ^ -9 C (2 nC).

2) Find the charges:

– the first charge: q1 = -q = -2 nC;

– second charge: q2 = -2q = -4 nC.

Answer: The first and second charges are equal to -2 nC and -4 nC, respectively.

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