Three point charges of 8 C, 3 C, and -5 C, are locate at the top, bottom left, and bottom right corners
respectively of an equilateral triangle of side 1Å. Find the magnitude and direction of the net force on the
3 C charge.
To find the net force on the 3 C charge, we need to calculate the electrostatic force between the 3 C charge and each of the other two charges, and then add up these individual forces as vectors.
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 between the charges
k is the Coulomb's constant, approximately 9 x 10^9 N m^2/C^2
q1 and q2 are the magnitudes of the charges in Coulombs
r is the separation distance between the charges in meters
First, let's calculate the force between the 3 C charge and the 8 C charge at the top corner of the equilateral triangle. The separation distance between them is equal to the side length of the triangle, which is given as 1Å (1 angstrom = 1 x 10^-10 meters).
F1 = (9 x 10^9 N m^2/C^2) * ((3 C) * (8 C)) / ((1 x 10^-10 m)^2)
Calculating F1, we get:
F1 ≈ 2.16 x 10^-6 N
Now, let's calculate the force between the 3 C charge and the -5 C charge at the bottom right corner of the equilateral triangle. The separation distance between them is also equal to the side length of the triangle, which is 1Å.
F2 = (9 x 10^9 N m^2/C^2) * ((3 C) * (-5 C)) / ((1 x 10^-10 m)^2)
Calculating F2, we get:
F2 ≈ -9 x 10^-7 N
Since forces are vector quantities, we need to consider their directions. The force F1 is attractive and pulls the 3 C charge towards the top corner of the triangle. The force F2 is repulsive and pushes the 3 C charge away from the bottom right corner.
To find the net force, we can add up these two forces as vectors:
Net Force = F1 + F2
Net Force ≈ (2.16 x 10^-6 N) + (-9 x 10^-7 N)
Calculating the net force, we get:
Net Force ≈ 1.26 x 10^-6 N
Therefore, the magnitude of the net force on the 3 C charge is approximately 1.26 x 10^-6 N. However, to determine the direction of the net force, we need to consider the vector nature of the forces involved.