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, . 

First lets set up two axes. Have  be to the right of charge 3 and 2 in the diagram and  be 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 the  direction). By using Coloumb's law, we can determine this force to be

 in the  direction 

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 the  direction). 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 that  and  create 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:

The force between the two charged particles is proportional to the product of their charges, according to Coulomb's Law. Whether the force is attractive or repulsive depends on the signs of the charges. Like signs will repel while opposite signs will attract.

Using Coulomb's Law to find the magnitude of the charge:

Therefore, the magnitude of the force has been discovered. Finally, since the signs are opposite ( and ), the force is attractive. Therefore the answer is:

The correct answer is the  charge and  charge  apart.

This results in the largest repulsive force according to the following equation:

 is the repulsive force,  is the magnitude of the charge,  is the distance between the charges and  is Coulomb's constant.

 and  charges placed  apart provides the greatest repulsive force.

The net force on the electron is the sum of the forces between the electron and each of the protons:

These forces are given by Coulomb's law:

Using the numbers given, we get:

Because opposite charges attract,  points left (the negative direction) and  points right (the positive direction).

Therefore, the net force is

Because this value is positive, the direction is rightward.

This question is very simple if you realize that the force experienced by both charges is equal.

The definition of the two electrostatic forces are given by Coulomb's law:

In this question, we can rewrite this equation in terms of our given system.

It doesn’t matter if the charges of the two particles are different; both particles experience the same force because the charges of both particles are accounted for in the electrostatic force equation (Coulomb's law). This conclusion can also be made by considering Newton's third law: the force of the first particle on the second will be equal and opposite the force of the second particle on the first.

Since the forces are equal, their ratio will be .

Two principal realizations help with solving this problem, both derived from Gauss’ law for electricity:

1) The excess charge on an ideal conducting sphere is uniformly distributed over its surface

2) A uniform shell of charge acts, in terms of electric force, as if all the charge were contained in a point charge at the sphere’s center

With these realizations, an application of Coulomb’s law answers the question. If  is the point charge outside the sphere, then the force  on  is:

In this equation, is Coulomb’s constant, is the excess charge on the spherical conductor, and is total distance in meters of  from the center of the conducting sphere.

Using the given values in this equation, we can calculate the generated force:

Coulomb's law gives the relationship between the force of an electric field and the distance between two charges:

The strength of the force will be inversely proportional to the square of the distance between the charges.

When the distance between the charges is doubled, the total force will be divided by four (quartered).