This is a question where knowing how to effectively sift through a problem statement and choose only the information you need will really help. We are given a bunch of values, but only need to know one thing, which is that the distance between the two charges is doubled.

Coulomb's law is as follows:

We can rewrite this for the initial and final scenarios:

We can divide one equation by the other to set up a ratio:

We know that the final radius is double the intial, which is written as:

Substituting this in we get:

Rerranging for the final force, we get:

Use Coulomb's law.

Plug in known values and solve.

Note that a positive value for electric force corresponds to a repulsive force. This should make sense since the charge on both particles are the same sign (positive).

Use Coulomb's law.

注意,两个电荷之间的电力of the same sign (both positive or both negative) is a positive value. This indicates a repulsive force.

Recall that Coulomb's law tells us that the magnitude of force between two point charges is given as:

Here,is force between two particles,are the charges of each of the two particles, and两个电荷间的距离。在我们这se,andare identical since each is the charge of a proton which is given as:, and

Thus, plug in known values and solve.

To determine if the force is attractive or repulsive, we only need to examine the sign of the charges. Since both protons have the same sign for their charge (positive charges) they will repel.

Use Coulomb's law to find the electric force between the charges:

The electric force between two point charges is given by Coulomb's law:

Now, plug in the given charges (both the same magnitude), the given constant, and the distance between the charges (in meters) to get our answer:

We are given all the necessary information to find the magnitude of the electric force by using Coulomb's law:

Whereis Coulomb's constant given by,andare the respective charges, andis the distance between the charges. In our case:

The method to solving Coulomb's law problems with electrostatic configurations is to find the magnitude of the force and then assign a direction based of what is known about the charges. Coulomb's law is given as:

Whereandare the two particles we are finding the force between andis the electric constant and is:

Notice that the distances betweenand是一样的吗and. Since the magnitudes of all charges are the same, that means that the magnitudes of the forces (not directions) are the same. So the force exerted onfromis the same magnitude as the force exerted onfrom.

A sketch of the forces is shown below:

Remember that there are always equal and opposite force pairs. We only care about the forces acting onand the last picture shows the two forces that act on it fromand. Notice that the vector arrows are of equal length (force magnitudes are equal) and in different directions. Coulomb forces obey the law of superposition and we can add them. Before we do that let's calculate the magnitude of the two forces pictured.

Remember to convert distances to meters and charge magnitudes to Coulombs so the units work out and you are not off by any factors of.

Both the red vector arrow and the blue vector arrow have magnitudes of. Notice in the diagram below that if the charges are spaced equidistant, the will form an equilateral triangle.

The angleis the same angle that each vector on the right has relative to the line drawn. In order to add the vectors together we need to separate the components of the vectors into their x- and y-components and add the respective components. This is where symmetry can be handy to make the problem easier. Since the particles are equidistant and the charge magnitudes are all equal, this lead to the force magnitudes to be equal. By inspection it can be shown that the y-components must be equal and opposite and therefore cancel.

This means that total magnitude of the force acting onis just the sum of the x-component forces. To get the x-components we can use the cosine of the angle. Since the angles are equal and the magnitudes are equal, the final answer will be:

The final answer is in the positive x-direction, denoted by the positive answer and theto indicate in the x-direction. The answer must have a magnitude and direction to describe the net force acting on the particle.

From Coulomb's Law:

Whereis the distance between point charges,, andandare charges of the electrons. In our case,.

First lets set up two axes. Havebe to the right of charge 3 and 2 in the diagram andbe above charges 1 and 2 in the diagram with charge 2 at the origin.

Coloumb's law tells us the force between point charges is

The net force on charge 2 can be determined by combining the force on charge 2 due to charge 1 and the force on charge 2 due to charge 3.

Since charge 1 and charge 2 are of opposite polarities, they have an attractive force; therefore, charge 2 experiences a force towards charge 1 (in thedirection). By using Coloumb's law, we can determine this force to be

in thedirection

Since charge 2 and 3 have the same polarities, they have a repulsive force; therefore, charge 2 experiences a force away from charge 2 (in thedirection). By using Coloumb's law, we can determine this force to be:

in the-direction

If we draw out these two forces tip to tail, we can construct the net force:

From this, we can see thatandcreate a right triangle with the net force on charge 2 as the hypotenuse. By using the Pythagorean theorem, we can calculate the magnitude of the net force: