Net Force on q5: Magnitude & Direction

[belleamie]

assume the charges 1-4 are fized ( q1=+3uC, q2=+4uC, q3=-3, q4=-4)
Find the net force felt by charge 5 (q5=-2uC) both magnitude and direction. I'm not sure wut equation to use?

 

[Chen]

I assume the charges are fixed in a square structure, and the fifth one is in the center of the square?

It doesn't really matter, what you need to do is find the force that each of the four charges exerts on the center charge. This force is defined as:
F_E = K\frac{q_1q_2}{r^2}
To find the net force, simply add the four vectors you got. You will notice that you have two pairs of forces that work along the same action line, add them first since it's easiest. Then you will be left with two force vectors, perpendicular to each other. Use pythagoras to find the magnitude of the net force and the trigonometric function tan to find its direction.

 

[M98Ranger]

To find the net force on charge 5, we can use Coulomb's Law, which states that the 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 equation for Coulomb's Law is F = k*q1*q2 / r^2, where k is the Coulomb's constant (9x10^9 N*m^2/C^2), q1 and q2 are the charges, and r is the distance between them.

In this case, we have four fixed charges (q1, q2, q3, q4) and one charge (q5) that we want to find the net force on. We can calculate the net force by finding the individual forces between q5 and each of the other charges, and then adding them together vectorially.

First, let's find the force between q5 and q1. Plugging in the values, we get F1 = (9x10^9 N*m^2/C^2)*(-2uC)*(+3uC) / r^2. Since the distance between q5 and q1 is not given, we can assume that it is the same as the distance between q5 and q4, which we will call r1. Similarly, the force between q5 and q2 is F2 = (9x10^9 N*m^2/C^2)*(-2uC)*(+4uC) / r^2, where r2 is the distance between q5 and q2.

Next, we can find the forces between q5 and q3 and q4 using the same equation. However, since q3 and q4 have negative charges, the forces will be repulsive. Thus, we have F3 = (9x10^9 N*m^2/C^2)*(-2uC)*(-3uC) / r^2 and F4 = (9x10^9 N*m^2/C^2)*(-2uC)*(-4uC) / r^2.

To find the net force, we need to add these four forces together vectorially. This means we need to find the x and y components of each force, and then add them separately. The x component of a force is given by F*cos(theta), where theta is the angle between the force vector and the x-axis. Similarly, the y component is given by F*sin