# AP Physics 1 : Electric Force Between Point Charges

## Example Questions

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### Example Question #1 : Electrostatics

Two point charges, each having a charge of +1C, are 2 meters apart. If the distance between them is doubled, by what factor does the force between them change?

The force between the charges remains constant

Explanation:

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:

### Example Question #1 : Electric Force Between Point Charges

What is the force exerted on a point charge of  by a point charge of  that is located  away?

Explanation:

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).

### Example Question #2 : Electrostatics

If we have 2 charges,  and , that are  apart, what is the force exerted on  by  if we know that  has a charge of  and  has a charge of ?

Explanation:

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.

### Example Question #1 : Electrostatics

Determine the magnitude of the electric force between 2 protons that are 3nm apart. Also determine if this force is attractive or repulsive.

; attractive

; repulsive

; repulsive

; repulsive

; repulsive

Explanation:

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.

### Example Question #4 : Electricity

A point charge of magnitude  is located 0.01m away from a point charge of magnitude . What is the electric force between the point charges?

Explanation:

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

### Example Question #3 : Electrostatics

A point charge of magnitude  is 2nm away from a point charge of identical charge. What is the electric force between the point charges?

Explanation:

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:

### Example Question #4 : Electrostatics

What is the magnitude of the electric force between two charged metals that are 3m apart, that have absolute value of the charges being 1C and 3C?

Explanation:

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:

### Example Question #5 : Electrostatics

Three charges are shown in the given figure. Find the net force on the "top" charge due to the other two (both magnitude and direction). Let  and assume all charges are  away from each other.

Let  be the bottom left particle,  be the top particle and  be the bottom right particle. Note the  axis.

Explanation:

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.

### Example Question #2 : Electric Force Between Point Charges

A mole of electrons have a charge of , which is called Faraday's constant. Given that Faraday's constant is , determine the electric force per mole exerted by  individual moles of electrons on one another separated by by . Assume charges are static. Use Coulomb's law, and assume that moles of electrons behave like a point charge.

Explanation:

From Coulomb's Law:

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

### Example Question #1 : Electric Force Between Point Charges

If , and , then what is the magnitude of the net force on charge 2?

Explanation:

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:

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