A 2.2 C charge is located on the x-axis at x = -1.5 m. A 5.4 C charge is located on the x-axis at x = 2.0m. A 3.5 C charge is at the origin. Find the net force acting on the 3.5 C charge.
To find the net force acting on the 3.5 C charge, we need to calculate the individual forces exerted on it by the other charges.
The force between two charges can be found using Coulomb's Law:
F = k * (q1 * q2) / r^2
where F is the force, k is the electrostatic constant (8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.
Let's calculate the forces individually:
1. Force exerted by the 2.2 C charge on the 3.5 C charge:
q1 = 2.2 C
q2 = 3.5 C
r = distance between them (which is the absolute value of the x-coordinate of the charge - the x-coordinate of the 3.5 C charge)
= |(-1.5 m) - (0 m)|
= 1.5 m
Plugging these values into Coulomb's Law:
F1 = (8.99 x 10^9 N m^2/C^2) * ((2.2 C * 3.5 C) / (1.5 m)^2)
2. Force exerted by the 5.4 C charge on the 3.5 C charge:
q1 = 5.4 C
q2 = 3.5 C
r = |(2.0 m) - (0 m)|
= 2.0 m
Plugging these values into Coulomb's Law:
F2 = (8.99 x 10^9 N m^2/C^2) * ((5.4 C * 3.5 C) / (2.0 m)^2)
To find the net force, we need to consider the direction of the forces. Since the 2.2 C charge is to the left of the origin and the 5.4 C charge is to the right of the origin, the net force will be the vector sum of the forces and will have both magnitude and direction.
To calculate the vector sum, we need to add the forces F1 and F2, taking into account their directions. Since the forces have opposite directions, we need to subtract the magnitude of F1 from the magnitude of F2 if F2 is greater, or vice versa if F1 is greater.
Now let's calculate the magnitudes of the forces F1 and F2:
Magnitude of F1 = |F1|
Magnitude of F2 = |F2|
Finally, the net force is the vector sum of F1 and F2:
Net force = F2 - F1 if F2 > F1
Net force = F1 - F2 if F1 > F2
By calculating these values, you can find the net force acting on the 3.5 C charge.