An equilateral triangle has sides of 0.15 m. Charges of -9.4, +8.0, and +2.5 µC are located at the corners of the triangle. Find the magnitude of the net electrostatic force exerted on the 2.5-µC charge.
To find the magnitude of the net electrostatic force exerted on the 2.5 µC charge, we need to consider the individual forces exerted by each charge and then use vector addition to find the net force.
The formula to calculate the electrostatic force between two charges is given by Coulomb's law:
F = k * ( |Q1 * Q2| / r^2 )
where F is the electrostatic force, k is the Coulomb's constant (9 × 10^9 N*m^2/C^2), Q1 and Q2 are the magnitudes of the two charges, and r is the distance between the charges.
Now, let's calculate the force exerted on the 2.5 µC charge by each of the other charges.
1. Force exerted by the -9.4 µC charge:
Q1 = 2.5 µC
Q2 = -9.4 µC
r = side length of the equilateral triangle = 0.15 m
Using Coulomb's law:
F1 = k * ( |Q1 * Q2| / r^2 )
2. Force exerted by the +8.0 µC charge:
Q1 = 2.5 µC
Q2 = 8.0 µC
r = side length of the equilateral triangle = 0.15 m
Using Coulomb's law:
F2 = k * ( |Q1 * Q2| / r^2 )
Now, to find the net force, we need to use vector addition. Because we are dealing with charges placed at the corners of an equilateral triangle, the net force will have both magnitude and direction.
To find the net force, we need to add the forces exerted by each charge as vectors. Since the triangle is equilateral, the angles between the sides of the triangle are 60°. Therefore, the angle between each force vector is 60°.
Using the law of cosines, we can find the magnitude of the net force:
|Net Force|^2 = F1^2 + F2^2 + 2 * F1 * F2 * cos(60°)
Finally, calculating the magnitude of the net force:
|Net Force| = sqrt( F1^2 + F2^2 + 2 * F1 * F2 * cos(60°) )
Plug in the values of F1 and F2 calculated earlier to find the magnitude of the net electrostatic force exerted on the 2.5 µC charge.