Question

A positive charge is fixed at point (−4,3) and a negative charge − is fixed at point (−4,0). Determine the net electric force ⃗ net acting on a positive test charge + at the origin (0,0) in terms of the given quantities and physical constants, including the permittivity of free space 0. Express the force using unit vector notation. Enter precise fractions rather than entering their approximate numerical values.

Answer 1

To calculate the net electric force on the positive test charge at the origin, we need to calculate the electric force exerted by each charge separately and then find the vector sum. The electric force between two point charges can be calculated using Coulomb's law.

Step-by-step explanation:

To calculate the net electric force on a positive test charge at the origin, we need to calculate the electric force exerted by each charge separately and then find the vector sum. The electric force between two point charges can be calculated using 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. The formula for the electric force is given by F = k * (q1 * q2) / r^2, where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.

Let's calculate the electric force exerted by the positive charge at (-4,3) on the positive test charge at the origin (0,0):

1. Calculate the distance between the two charges: r = sqrt((0 - (-4))^2 + (0 - 3)^2) = sqrt(16 + 9) = sqrt(25) = 5.
2. Calculate the electric force: F1 = k * (q1 * q_test) / r^2, where q1 is the charge of the positive charge and q_test is the charge of the test charge. Since the test charge is positive, q_test = 1 (assuming unit charge).
3. Plug in the values: F1 = k * (q1 * q_test) / r^2 = k * (1 * q1) / (5^2).

Similarly, we can calculate the electric force exerted by the negative charge at (-4,0) on the positive test charge at the origin:

1. Calculate the distance between the two charges: r = sqrt((0 - (-4))^2 + (0 - 0)^2) = sqrt(16) = 4.
2. Calculate the electric force: F2 = k * (q2 * q_test) / r^2, where q2 is the charge of the negative charge.
3. Plug in the values: F2 = k * (q2 * q_test) / r^2 = k * ((-1) * q_test) / (4^2).

Finally, we can find the net electric force by summing the individual forces, taking into account their direction. Since the positive charge is repelling the positive test charge and the negative charge is attracting the positive test charge, the net force will have a direction towards the negative charge. The net force can be calculated using vector addition, taking into account the x and y components of the forces.