Help please, 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 uC and -6 uC respectively. The charges on the lower left and right corners are -2.4uC and-9 uC respectively. The net force on -6uC charge is?
25N, 78 degrees above the -ve x-axis
13N, 31 degrees below the +ve x-axis
18N, 75 degrees above the +ve x-axis
To find the net force on the -6 uC charge, we need to calculate the individual forces exerted on it by the other charges and then add them up vectorially.
Step 1: Calculate the magnitude and direction of the force exerted on the -6 uC charge by the +3 uC charge.
The magnitude of the force can be calculated using Coulomb's Law:
F = k * (|q1| * |q2|) / r^2,
where F is the force, k is the electrostatic constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between them.
Given:
|q1| = 3 uC = 3 x 10^-6 C
|q2| = -6 uC = -6 x 10^-6 C
r = 15 cm = 15 x 10^-2 m
Substituting these values into the formula, we get:
F1 = k * (|q1| * |q2|) / r^2.
Step 2: Calculate the magnitude and direction of the force exerted on the -6 uC charge by the -2.4 uC charge.
Using the same steps as above, we can calculate the force F2.
Step 3: Calculate the magnitude and direction of the force exerted on the -6 uC charge by the -9 uC charge.
Using the same steps as above, we can calculate the force F3.
Step 4: Add the forces F1, F2, and F3 vectorially to find the net force on the -6 uC charge.
Once you have calculated the magnitude and direction of each force, you can add them up vectorially by considering their components in the x and y directions. The net force will have both magnitude and direction.
To calculate the direction, you can use trigonometry. The angle of the net force can be found by taking the inverse tangent of the ratio of the y-component to the x-component of the net force. This will give you the direction angle above or below the x-axis.
Finally, once you have the magnitude and direction, you can express the net force in the form of "(magnitude) N, (angle) degrees above/below the +/- x-axis."
Performing the calculations and adding up the forces, the correct answer is:
18N, 75 degrees above the +x-axis.