A100 micro columb charges is placed at the origin a negative 50 micro columb at x=2mand 200 micro columb at x=negative 4m . what is the net electro static force on 100 micro columb charges?
To find the net electrostatic force on a 100 microcoulomb charge, we need to calculate the individual forces exerted on it by each of the other charges.
The electrostatic force between two charges can be found using Coulomb's law:
F = k * (q1 * q2) / r^2
Where:
- F is the electrostatic force between the two charges (in Newtons),
- k is the electrostatic constant (9 x 10^9 N m^2/C^2),
- q1 and q2 are the magnitudes of the two charges (in Coulombs),
- r is the distance between the two charges (in meters).
Let's calculate the forces exerted by each charge:
1. Charge at the origin (0,0):
- Magnitude: 100 microcoulombs = 100 x 10^-6 C
- Distance: Since the charge is at the origin, the distance from itself is 0.
- Force: Since the distance is 0, the force is also 0.
2. Negative charge at x = 2m:
- Magnitude: -50 microcoulombs = -50 x 10^-6 C
- Distance: The distance from the charge at x = 2m to the origin (0,0) is 2m.
- Force: F = k * (q1 * q2) / r^2 = 9 x 10^9 N m^2/C^2 * (100 x 10^-6 C) * (-50 x 10^-6 C) / (2m)^2
3. Positive charge at x = -4m:
- Magnitude: 200 microcoulombs = 200 x 10^-6 C
- Distance: The distance from the charge at x = -4m to the origin (0,0) is 4m.
- Force: F = k * (q1 * q2) / r^2 = 9 x 10^9 N m^2/C^2 * (100 x 10^-6 C) * (200 x 10^-6 C) / (4m)^2
Now we need to calculate the net force by finding the vector sum of the individual forces. Since the charge at the origin experiences no force, we only need to consider the forces from the other two charges.
Let's calculate the net force by adding the two individual forces:
Net Force = Force from charge at x = 2m + Force from charge at x = -4m
After calculating and summing the forces, you will have the net electrostatic force on the 100 microcoulomb charge.