Three point charges are fixed on the x-axis: 2.9×10−6 C at x = −0.45 m, −9.3×10−6 C at the origin, and 9.1×10−6 C at x = 0.32 m. Find the electrostatic force acting on the charge at the origin due to the other two charges. Let a positive value indicate a force in the positive x direction, and a negative value indicate a force in the negative x direction.
To find the electrostatic force acting on the charge at the origin due to the other two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two point charges is directly proportional to the product of the 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 electrostatic force
k is the electrostatic constant (k = 8.99 * 10^9 N m^2/C^2)
q1 and q2 are the charges
r is the distance between the charges
Let's first calculate the force between the charge at the origin and the charge at -0.45m.
q1 = -9.3 * 10^(-6) C
q2 = 2.9 * 10^(-6) C
r1 = 0.45 m
Using Coulomb's Law:
F1 = (8.99 * 10^9 N m^2/C^2) * ((-9.3 * 10^(-6) C) * (2.9 * 10^(-6) C)) / (0.45 m)^2
Let's now calculate the force between the charge at the origin and the charge at 0.32m.
q1 = -9.3 * 10^(-6) C
q2 = 9.1 * 10^(-6) C
r2 = 0.32 m
Using Coulomb's Law:
F2 = (8.99 * 10^9 N m^2/C^2) * ((-9.3 * 10^(-6) C) * (9.1 * 10^(-6) C)) / (0.32 m)^2
Now, let's find the net force acting on the charge at the origin by adding the forces F1 and F2, taking into account their directions:
- If both forces are positive or negative, we add them algebraically.
- If one force is positive and the other is negative, we subtract them.
Let's calculate the net force:
Net F = F1 + F2
This will give us the electrostatic force acting on the charge at the origin.
To find the electrostatic force acting on the charge at the origin due to the other two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is given as:
F = k * (|q1 * q2|) / r^2
where F is the magnitude of the electrostatic force, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, we have three charges: q1 = 2.9 x 10^-6 C, q2 = -9.3 x 10^-6 C, and q3 = 9.1 x 10^-6 C.
To find the net force on the charge at the origin, we need to calculate the forces between the origin charge and the two charges on either side of it, and then sum the two forces.
Let's start with the force between the origin charge and the charge at x = -0.45 m:
r1 = distance between the origin and x = -0.45 m = 0.45 m
F1 = k * (|q2 * q1|) / r1^2
= (8.99 x 10^9 N m^2/C^2) * (9.3 x 10^-6 C) * (9.3 x 10^-6 C) / (0.45 m)^2
Next, let's calculate the force between the origin charge and the charge at x = 0.32 m:
r2 = distance between the origin and x = 0.32 m = 0.32 m
F2 = k * (|q3 * q1|) / r2^2
= (8.99 x 10^9 N m^2/C^2) * (9.1 x 10^-6 C) * (9.3 x 10^-6 C) / (0.32 m)^2
Finally, to get the net force on the charge at the origin, we add the two forces together:
Net force = F2 - F1
Based on the given values, you can now substitute the values, calculate F1 and F2, and find the net force acting on the charge at the origin. If the net force is positive, it indicates a force in the positive x direction. If it is negative, it indicates a force in the negative x direction.