Three charges are at the corners of a rectangle with side L1 = 0.04 m and L2 = 0.015 m as shown. If q1 = 1.3 microCoulombs, q2 = 2.8 microCoulombs, and q3 = 3.3 microCoulombs, what is the magnitude of the force on q2
To find the magnitude of the force on q2, we need to calculate the electrostatic force between q2 and the other charges. The electrostatic force between two charges can be calculated using Coulomb's Law:
F = (k * |q1 * q2|) / r^2
where F is the force, k is the electrostatic constant (k = 9 x 10^9 Nm^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 arranged in a rectangle. Let's label the charges as follows:
q1 is at the top left corner,
q2 is at the bottom right corner,
q3 is at the top right corner.
To find the force on q2, we need to calculate the forces between q2 and q1, and between q2 and q3, and then find the net force acting on q2.
Step 1: Calculating the force between q2 and q1
The distance between q2 and q1 is the diagonal of the rectangle. We can use the Pythagorean theorem to find this distance:
diagonal^2 = L1^2 + L2^2
distance (r1) = sqrt(L1^2 + L2^2)
Now we can calculate the force between q2 and q1:
F1 = (k * |q2 * q1|) / r1^2
Step 2: Calculating the force between q2 and q3
The distance between q2 and q3 is the side length L2. We can directly use this distance to calculate the force between q2 and q3:
F3 = (k * |q2 * q3|) / L2^2
Step 3: Summing up the forces
The net force on q2 is the vector sum of the forces F1 and F3. Since force F1 is diagonal and force F3 is perpendicular to L2, these forces act at right angles to each other and can be added using the Pythagorean theorem:
F_net = sqrt(F1^2 + F3^2)
Finally, plug in the values of the charges and distances into the equations, and calculate the magnitude of the force on q2.