To answer this question, we need to understand the concept of standing waves. A standing wave is a wave that exhibits both nodes and antinodes. A node is a fixed position where there is no displacement from the wave, and an antinode is a point of maximum displacement of the wave.

A standing wave can result from two individual waves traveling in opposite directions and interfering with each other. For instance, when a wave traveling through one medium (such as the air in the pipe) hits an interface that is denser (such as the end of the pipe), the wave will reflect back. However, this reflected wave will be shifted  out of phase. As a result, the reflected wave will interact with the incident wave, and the two will interfere. This interference takes on a specific pattern in which there is destructive interference in the location of nodes, and constructive interference in the location of the antinodes. In such a situation, it doesn't appear that the wave is traveling at all, but rather it looks as if it's standing still, hence the name standing wave.

To solve this question, we need to use the expression for a pipe closed at one end and open at the other.

With this expression, we just need to plug in the values given to us in the question to solve for the length of the pipe.

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.

Note that the electric force between two charges 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  is the distance between the two charges. In our case,  and  are 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: 

Where  is Coulomb's constant given by ,  and  are the respective charges, and  is 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:

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

Notice that the distances between  and  is the same as the  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 on  from  is the same magnitude as the force exerted on  from .

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 on  and the last picture shows the two forces that act on it from  and . 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 angle  is 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 on  is 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 the  to 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: 

Where  is the distance between point charges, , and  and  are charges of the electrons. In our case, .