Three charges are fixed to an x, y coordinate system. A charge of +19 µC is on the y axis at y = 2.8 m. A charge of -13 µC is at the origin. Last, a charge of +47 µC is on the x axis at x = +2.8 m. Determine the magnitude and direction of the net electrostatic force on the charge at x = +2.8 m. Specify the direction relative to the −x axis.
To determine the magnitude and direction of the net electrostatic force on the charge at x = +2.8 m, we can use Coulomb's law.
Coulomb's law states that the electrostatic force between two point charges 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 electrostatic force, k is Coulomb's constant (9.0 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, we have three charges fixed in an x, y coordinate system. Let's label them as follows:
Charge 1: +19 µC at (0, 2.8)
Charge 2: -13 µC at (0, 0)
Charge 3: +47 µC at (2.8, 0)
To find the net electrostatic force on the charge at x = +2.8 m, we need to calculate the individual forces exerted by charges 1 and 3 on the charge at x = +2.8 m and add them together.
First, let's calculate the force exerted by charge 1 on the charge at x = +2.8 m.
Distance between charge 1 and the charge at x = +2.8 m: r1 = 2.8 m (same as the x-coordinate)
Charge of charge 1: q1 = +19 µC
Charge of charge at x = +2.8 m: q = +47 µC
Using Coulomb's law:
F1 = k * (q1 * q) / r1^2
Next, let's calculate the force exerted by charge 3 on the charge at x = +2.8 m.
Distance between charge 3 and the charge at x = +2.8 m: r3 = 2.8 m (same as the x-coordinate)
Charge of charge 3: q3 = +47 µC
Using Coulomb's law:
F3 = k * (q3 * q) / r3^2
Finally, to find the net electrostatic force on the charge at x = +2.8 m, we add the forces exerted by charge 1 and charge 3:
Net force = F1 + F3
Calculating these forces and adding them will give us the magnitude of the net force. To find the direction of the net force relative to the -x axis, we need to determine the angle between the net force vector and the -x axis. This can be done using trigonometry.
I hope this explanation helps you understand how to calculate the magnitude and direction of the net electrostatic force on the charge at x = +2.8 m! Let me know if you have any other questions.