Step-by-step explanation:
To solve this problem, we will use the principle of Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Given:
Charge 1 (q1) = -3.40 nC
Charge 2 (q2) = 2.45 nC
Charge 3 (q3) = 5.00 nC
Position of charge 1: (0, 0)
Position of charge 2: (0, 4.25 cm)
Position of charge 3: (2.90 cm, 4.25 cm)
a. To find the x and y components of the total force exerted on charge 3 by the other two charges, we can break down the net force into horizontal (x-direction) and vertical (y-direction) components.
The force exerted on charge 3 by charge 1 (F13) can be calculated as:
F13 = (k * |q1 * q3|) / r^2
where k is Coulomb's constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q3 are the charges, and r is the distance between them.
Similarly, the force exerted on charge 3 by charge 2 (F23) can be calculated.
Once we have F13 and F23, we can find the x and y components by multiplying the magnitude of each force by the cosine and sine of the angle between the force vector and the x-axis or y-axis, respectively.
b. The magnitude of the total force can be calculated using the pythagorean theorem:
|F| = sqrt(Fx^2 + Fy^2)
c. The direction of the force can be determined by finding the angle between the force vector and the positive x-axis using the arctan function:
θ = arctan(Fy / Fx)
By calculating these values, we can solve the problem.
Note: We need to convert the given distances in centimeters (cm) to meters (m) to maintain consistency with the units used in Coulomb's law.
Please provide the value of q1, which was not given in the question, so that we can proceed with the calculations.