Final answer:
To calculate the x and y components of the total force on the third charge, we apply Coulomb's law individually for the force from each of the other charges and then sum these components, considering the sign and direction of each.
Step-by-step explanation:
To find the x and y components of the total force exerted on the 5.00 nC charge by the other two charges, we use Coulomb's law, which states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. This law is given by the equation F = k * |q1 * q2| / r^2, where k is Coulomb's constant (8.99 x 10^9 N*m^2/C^2), q1 and q2 are the amounts of the charges, and r is the distance between the charges.
For the charge at the origin (-3.50 nC), we find the distance to the third charge (5.00 nC) using Pythagoras' theorem since the charge is located on the x-axis at 3.05 cm away. The resulting distance is √((3.05 cm)^2 + (4.50 cm)^2). We then calculate the force and break it into its x and y components based on the angle to the horizontal.
Similarly, the charge on the y-axis (2.10 nC) is directly vertically above the third charge, so we only need to find the y-component of the force it exerts, as there is no x-component in this case.
Summing the x components from both forces and the y components gives us the total force exerted in both the x and y directions. However, because there are both positive and negative charges involved, we need to be mindful of the direction of each force component when performing the summation.