Three charged particles are placed at the corners of an equilateral triangle of side d = 1.40 m (Fig. 16-53). The charges are Q1 = +4.0 µC, Q2 = -7.0 µC, and Q3 = -6.0 µC. Calculate the magnitude and direction of the net force on each due to the other two.
To calculate the magnitude and direction of the net force on each charge due to the other two charges, you can use Coulomb's Law.
Coulomb's Law states that the magnitude of the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|Q1 * Q2|) / r^2
Where:
F is the magnitude of the force between the charges,
k is the electrostatic constant (k ≈ 9 x 10^9 Nm^2/C^2),
Q1 and Q2 are the charges on the particles,
|r| is the distance between the particles' positions.
To find the net force on a charge, you need to calculate the individual forces due to each of the other charges, and then vectorially add them up.
Let's start by calculating the net force on Q1 due to charges Q2 and Q3.
1. Calculate the force between Q1 and Q2:
F12 = k * (|Q1 * Q2|) / r^2
F12 = (9 x 10^9 Nm^2/C^2) * (|4.0 µC * (-7.0 µC)|) / (1.40 m)^2
Similarly, calculate the force between Q1 and Q3:
F13 = k * (|Q1 * Q3|) / r^2
F13 = (9 x 10^9 Nm^2/C^2) * (|4.0 µC * (-6.0 µC)|) / (1.40 m)^2
2. Combine the forces F12 and F13 vectorially. Since the charges Q2 and Q3 are placed at the corners of an equilateral triangle, the angle between the two forces is 120 degrees.
Using the law of cosines to find the magnitude of the net force:
Fnet1 = sqrt(F12^2 + F13^2 + 2 * F12 * F13 * cos(120°))
The direction of the net force can be found using the law of sines:
θ1 = sin^(-1)((F12 * sin(120°)) / Fnet1)
Repeat the above steps to find the net forces and their directions for charges Q2 and Q3 due to each other.
Remember to use the appropriate charges and distances for each calculation.