Four charges are placed at the four corners of a square of side 15 cm. The charges on the upper left and right corners are +3 μC and -6 μC respectively. The charges on the lower left and right corners are -2.4 μC and -9 μC respectively. The net electric force on -9 μC charge is:
the answer choices are
18 N, 750 below the positive x-axis
18 N, 750 below the negative x- axis
18 N, 750 above the negative x- axis
18 N, 750 above the positive x- axis
18 N, 750 above the + x- axis
To find the net electric force on the -9 μC charge, we need to consider the forces due to each of the other three charges. The electric force between two charges can be calculated using Coulomb's law:
F = k * (|q1 * q2|) / r^2
where F is the magnitude of the electric force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's break down the problem step by step:
1. Calculate the electric force due to the +3 μC charge on the -9 μC charge:
F1 = k * (|q1 * q2|) / r^2 = (9 x 10^9 Nm^2/C^2) * (|-9 μC * 3 μC|) / (15 cm)^2
The distance between these two charges is the length of the diagonal of the square, which can be calculated using Pythagoras' theorem:
Diagonal = sqrt(15 cm^2 + 15 cm^2) = sqrt(2 * 15^2) = sqrt(2 * 225) = sqrt(450) ≈ 21.213 cm
Plugging in the values, we get:
F1 = (9 x 10^9 Nm^2/C^2) * (|-9 μC * 3 μC|) / (21.213 cm)^2
2. Calculate the electric force due to the -2.4 μC charge on the -9 μC charge:
F2 = k * (|q1 * q2|) / r^2 = (9 x 10^9 Nm^2/C^2) * (|-9 μC * -2.4 μC|) / (15 cm)^2
The distance between these two charges is the side length of the square, which is 15 cm.
Plugging in the values, we get:
F2 = (9 x 10^9 Nm^2/C^2) * (|-9 μC * -2.4 μC|) / (15 cm)^2
3. Calculate the electric force due to the -6 μC charge on the -9 μC charge:
F3 = k * (|q1 * q2|) / r^2 = (9 x 10^9 Nm^2/C^2) * (|-9 μC * -6 μC|) / (21.213 cm)^2
The distance between these two charges is also the length of the diagonal of the square, which we previously calculated as 21.213 cm.
Plugging in the values, we get:
F3 = (9 x 10^9 Nm^2/C^2) * (|-9 μC * -6 μC|) / (21.213 cm)^2
4. Calculate the net electric force on the -9 μC charge:
Since forces are vector quantities, we need to consider both their magnitudes and directions. The net electric force is the vector sum of F1, F2, and F3. To determine the direction, we need to analyze the charges' positions.
Looking at the diagram, the +3 μC charge and the -2.4 μC charge are diagonally opposite to the -9 μC charge. Thus, the forces exerted by these charges will be in opposite directions and cancel each other out. The force due to the -6 μC charge is along the positive x-axis.
Neglecting the canceling forces, the net force will be:
NetF = F3 = (9 x 10^9 Nm^2/C^2) * (|-9 μC * -6 μC|) / (21.213 cm)^2
Now, you can calculate the numerical value of NetF and determine its direction. Comparing it with the given answer choices, you can determine the correct option.