An equilateral triangle has sides of 0.17 m. Charges of -9.0, +8.0, and +2.2 µC are located at the corners of the triangle. Find the magnitude of the net electrostatic force exerted on the 2.2-µC charge.
Add as vectors the forces due to the charges at the opposite corners. This requires a knowledge of Coulomb's law and how to add vectors. I assume you are familiar with both.
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10 years later.
To find the magnitude of the net electrostatic force exerted on the 2.2-µC charge, we can use Coulomb's law and apply it to each pair of charges separately. Then, we'll find the vector sum of all the forces acting on the 2.2-µC charge.
Coulomb's law states that the magnitude of the electrostatic force between two point charges is given by:
F = (k * |q1 * q2|) / r^2
Where:
F is the magnitude of the electrostatic force
k is the Coulomb's constant (k ≈ 8.99 x 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 force exerted on the 2.2-µC charge by each of the other charges:
1) With -9.0 µC charge:
F1 = (k * |(2.2 x 10^-6) * (-9.0 x 10^-6)|) / (0.17)^2
2) With +8.0 µC charge:
F2 = (k * |(2.2 x 10^-6) * (8.0 x 10^-6)|) / (0.17)^2
The forces F1 and F2 are acting in different directions, so we need to consider their vectors. Since the charges are arranged in an equilateral triangle, the forces have angles of 120 degrees with respect to each other.
To calculate the net force, we need to find the vector sum of F1 and F2. We can use the Pythagorean theorem and trigonometry to do this.
Let's calculate the net force:
Fnet = sqrt((F1^2 + F2^2 + 2 * F1 * F2 * cos(120°)))
Finally, the magnitude of the net electrostatic force exerted on the 2.2-µC charge is equal to Fnet.
Plug in the values of F1, F2, and calculate the net force Fnet to get the answer.