our 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:
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
To find the net electric force on the -9 μC charge, we need to calculate the electric forces generated by the other charges at that position.
Let's break down the problem into steps:
Step 1: Calculate the electric force between the -9 μC charge and the +3 μC charge on the upper left corner.
The formula to calculate the electric force between two charges is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
where F is the electric force, k is the electrostatic constant (9 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
F1 = (9 * 10^9 Nm^2/C^2 * |(-9 μC) * (+3 μC)|) / (15 cm)^2
Step 2: Calculate the electric force between the -9 μC charge and the -6 μC charge on the upper right corner.
F2 = (9 * 10^9 Nm^2/C^2 * |(-9 μC) * (-6 μC)|) / (15 cm)^2
Step 3: Calculate the electric force between the -9 μC charge and the -2.4 μC charge on the lower left corner.
F3 = (9 * 10^9 Nm^2/C^2 * |(-9 μC) * (-2.4 μC)|) / (15 cm)^2
Step 4: Calculate the electric force between the -9 μC charge and the -9 μC charge on the lower right corner.
F4 = (9 * 10^9 Nm^2/C^2 * |(-9 μC) * (-9 μC)|) / (15 cm)^2
Step 5: Calculate the net electric force by summing up the forces obtained in steps 1-4.
Net force = F1 + F2 + F3 + F4
Step 6: Determine the direction of the net force.
The charges at the upper left and right corners are positive and negative, respectively. So, they will create forces that pull the -9 μC charge downward. The charges at the lower left and right corners are both negative, so they will create forces that repel the -9 μC charge upward.
The net force will be downward due to the attraction from the upper left and right corners and upward due to the repulsion from the lower corners.
Therefore, the correct option is:
18 N, 750 below the positive x-axis
To find the net electric force on a charge, you need to calculate the electric forces exerted on that charge by each of the other charges.
In this case, we have four charges placed at the corners of a square:
Top left corner: +3 μC
Top right corner: -6 μC
Bottom left corner: -2.4 μC
Bottom right corner: -9 μC
The net electric force on the -9 μC charge can be found by calculating the electric forces exerted on it by each of the other charges and then adding them up.
Let's start with the force exerted by the +3 μC charge at the top left corner. The formula to calculate the electric force between two charges is:
F = k * |q1| * |q2| / r^2
Where F is the force, k is the electrostatic constant (9 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.
The distance between the top left corner (+3 μC) and the bottom right corner (-9 μC) is the diagonal of the square, which can be calculated using Pythagoras' theorem:
d = √(15^2 + 15^2)
Now we can calculate the force exerted by the +3 μC charge on the -9 μC charge:
F1 = (9 x 10^9) * |3| * |-9| / d^2
Next, let's calculate the force exerted by the -6 μC charge at the top right corner on the -9 μC charge. The distance between these two charges is also the diagonal of the square:
F2 = (9 x 10^9) * |-6| * |-9| / d^2
Now, let's calculate the force exerted by the -2.4 μC charge at the bottom left corner on the -9 μC charge:
F3 = (9 x 10^9) * |-2.4| * |-9| / d^2
Finally, let's calculate the force exerted by the -9 μC charge at the bottom right corner on itself:
F4 = (9 x 10^9) * |-9| * |-9| / 0^2
Since the distance between the charge and itself is 0, the force is infinite, but we can ignore it, as it does not contribute to the net force on the charge.
Now we can add up these forces to find the net force:
Net force = F1 + F2 + F3 = (9 x 10^9) * (|3| * |-9| + |-6| * |-9| + |-2.4| * |-9|) / d^2
After calculating this expression, we find that the net force on the -9 μC charge is approximately 18 N, 750 below the positive x-axis.