Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle, as the drawing shows. The magnitude of each of the charges is 4.0 µC, and the lengths of the sides of the triangle are 4.7 cm. Calculate the magnitude of the net force that each charge experiences.

Where is the answer?

To calculate the magnitude of the net force that each charge experiences, we can use Coulomb's law. Coulomb's law states that the magnitude of the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

In this case, we have three charges arranged in an equilateral triangle. The negative charge will experience a force due to the repulsion from the two positive charges. Let's call the magnitude of the positive charges Q and the magnitude of the negative charge -Q.

First, let's calculate the distance between the charges. Since the triangle is equilateral, all sides have the same length. The length of each side of the triangle is 4.7 cm.

Now, let's calculate the net force on each charge. We'll consider the positive charges first:

The positive charges are at the corners of the triangle. To calculate the force on one of the positive charges, we need to consider the force due to the other positive charge and the force due to the negative charge.

The force between the two positive charges is repulsive because they have the same charge. So the force between them is given by Coulomb's law:

F_pp = k * (Q * Q) / (d * d)

where k is Coulomb's constant, Q is the magnitude of the charge, and d is the distance between the charges.

Next, let's calculate the force on one of the positive charges due to the negative charge. The force between the positive and negative charges is attractive because they have opposite charges. So the force between them is also given by Coulomb's law:

F_pn = k * (Q * (-Q)) / (d * d)

Note that the negative charge attracts the positive charge.

The net force on each positive charge is the vector sum of these two forces. Since the charges are arranged in an equilateral triangle, the net force on each positive charge is directed towards the center of the triangle. Therefore, the magnitude of the net force on each positive charge is given by:

|F_net_p| = √((F_pp + F_pn)²)

Finally, since the magnitude of the net force on each positive charge is the same, the magnitude of the net force on each charge is twice the magnitude of the net force on each positive charge.

So, to find the magnitude of the net force on each charge, we need to substitute the given values of Q, d, and k into the equations and perform the calculations.

Let's calculate it step by step:

1. Calculate the distance between the charges (d):
The length of each side of the equilateral triangle is given as 4.7 cm.

2. Substitute the given values and calculate the forces:
Use Coulomb's law with the calculated distance to calculate F_pp and F_pn.

3. Calculate the magnitude of the net force on each positive charge:
Find the vector sum of F_pp and F_pn and take its magnitude.

4. Calculate the magnitude of the net force on each charge:
Multiply the magnitude of the net force on each positive charge by 2, as they experience the same net force.

By following these steps, you'll be able to find the magnitude of the net force that each charge experiences.