physics question

Question

Use these numbers: Q₂ = -500 nC. When the second particle is placed on the x-axis at x = +27.0 cm, it experiences a force of 1.20 N in the positive x-direction. When the second particle is moved to x = +36.0 cm on the x-axis, it experiences a force of 3.50 N in the negative x-direction. Determine the location of the mystery charge.

x = _______ cm

Answer 1

You know that the mystery charge must be positive and between 27 and 36 cm: Let x be the distance above 27. (in m for Coulomb's law and L = .09m)

k_eQ(500 x 10^-9 C)/x² = 1.2 and k_eQ(500 x 10^-9C)/(L-x)² = 3.5

Take the ratio of these equations in order to simplify: (ratio allows us to solve for x in cm)

(9-x)²/x² = 1.2/3.5

Now multiply out and use quadratic formula for x.

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