Three charges are fixed to an x, y coordinate system. A charge of +12 µC is on the y axis at y = +3.0 m. A charge of -14 µC is at the origin. Lastly, a charge of +50 µC is on the x axis at x = +3.0 m. Determine the magnitude and direction of the net electrostatic force on the charge at x = +3.0 m. Specify the direction relative to the -x axis.
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�‹ below the -x axis?
To determine the magnitude and direction of the net electrostatic force on the charge at x = +3.0 m, we need to calculate the individual forces due to each charge and then add them vectorially.
The electrostatic force between two charges is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
- F is the magnitude of the force
- k is the electrostatic constant (k = 8.99 * 10^9 N m^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
Let's calculate the forces between the charge at x = +3.0 m and the other charges:
1. Force from the +12 µC charge on the y-axis:
The distance between the charge at x = +3.0 m and the +12 µC charge is the horizontal distance: r1 = 3.0 m.
The force between them can be calculated as:
F1 = (k * |q1 * q2|) / r1^2
F1 = (8.99 * 10^9 N m^2/C^2) * [ (12 * 10^-6 C) * (-50 * 10^-6 C) ] / (3.0 m)^2
2. Force from the -14 µC charge at the origin:
The distance between the charge at x = +3.0 m and the -14 µC charge at the origin is the hypotenuse of a right triangle: r2 = √((3.0 m)^2 + (3.0 m)^2) = √18 m ≈ 4.24 m.
The force between them can be calculated as:
F2 = (k * |q1 * q2|) / r2^2
F2 = (8.99 * 10^9 N m^2/C^2) * [ (14 * 10^-6 C) * (50 * 10^-6 C) ] / (4.24 m)^2
Now, we can calculate the net force vectorially by adding these forces.
Since the force from the charge on the y-axis is purely vertical and the force from the charge at the origin has both vertical and horizontal components, we only need to add the vertical forces:
Net force = F1 + F2
Next, we determine the direction of the net force.
Since the net force is in the negative y-direction, it is below the -x axis.
Therefore, the magnitude of the net electrostatic force on the charge at x = +3.0 m is the magnitude of the calculated net force, and the direction of the net force is below the -x axis.