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).

Use Coulomb's Law

Plug in known values and solve.

A negative value for electric force indicates an attractive force. This makes sense since our two charges have opposite signs. Since we're asked for magnitude, all answer choices are positive.

Use Coulomb's law.

Plug in known values and solve.

Note that this force is positive, which means it's repulsive.

Use Coulomb's law.

Plug in known values and solve.

Note that this force is positive, which means that it's repulsive.