We can calculate the net force on the point charge by summing up the individual forces due to the two charges. The force between two charges is given by Coulomb's law:
F = k * q1 * q2 / r^2
where F is the force, k is the electrostatic constant (approximately equal to 8.99 x 10^9 N * m^2 / C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's denote the x-coordinate of the point where the net force is zero as x. The force exerted by charge 1 on the point charge is:
F1 = k * (q1 * q3) / (x - x1)^2
The force exerted by charge 2 on the point charge is:
F2 = k * (q2 * q3) / (x2 - x)^2
Since the net force is zero, we have:
F1 + F2 = 0
Substituting the expressions for F1 and F2, we get:
k * (q1 * q3) / (x - x1)^2 + k * (q2 * q3) / (x2 - x)^2 = 0
Now, we can substitute the given values for q1, q2, x1, and x2:
k * (3.94 * 10^-6 * 0.3) / (x + 4.7)^2 + k * (6.14 * 10^-6 * 0.3) / (12.2 - x)^2 = 0
Simplifying the equation, we get:
(3.94 * 10^-6 * 0.3) / (x + 4.7)^2 + (6.14 * 10^-6 * 0.3) / (12.2 - x)^2 = 0
Now, we can solve this equation for x.
charge 1 is 3.94 µC and is located at x₁ = -4.7 m, and charge 2 is 6.14 µC and is at x2 = 12.2 m. What is the x-coordinate of the point at which the net force on a point charge of 0.300 μC is zero?
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