# AP Physics C Electricity : Using Coulomb's Law

## Example Questions

### Example Question #1 : Electricity And Magnetism Exam

We have a point charge of . Determine the electric field at a distance of  away from that charge.

Explanation:

Coulomb's law for the electric field from point charges is , where we know the values of the following variables.

Using these values, we can solve for the electric field.

### Example Question #1 : Using Coulomb's Law

Two positive point charges of  and  are place at a distance  away from each other, as shown below. If a positive test charge, , is placed in between, at what distance away from  will this test charge experience zero net force?

Explanation:

To find the location at which the test charge experience zero net force, write the net force equation as , where  is the force on the test charge from , and  is the force on the same test charge from . Using Coulomb's law, we can rewrite the force equation and set it equal to zero.

In this equation, the distance, , is how far away the test charge is from , while  represents how far away the test charge is from .  Now, we simplify and solve for .

Cross-multiply.

We can cancel and . We do not need to know these values in order to solve the question.

Now that we have isolated , we can plug in the values given in the question and solve.

### Example Question #1 : Electricity And Magnetism Exam

You are standing on top of a very large positively charged metal plate with a surface charge of .

Assuming that the plate is infinitely large and your mass is , how much charge does your body need to have in order for you to float?

Explanation:

Consider the forces that are acting on you. There is the downward (negative direction) force of gravity, . In order for you to float, there has to be an upward (positive direction) force, and that upward force is coming from the metal plate, . To show that you would float, the net force equation is written as , where  is the charge on you.

For plates that are charged, know that .

Knowing this, the force equation becomes .

Solve for .

Now we can plug in our given values, and solve for the charge.

### Example Question #1 : Electricity

A point charge of  exerts a force of  on another charge with . How far apart are the two charges?

Explanation:

To find the distance between the two charges, use Coulomb's Law.

Since we want to find distance, , we solve for .

We know the values of the force and the two charges.

We can plug in these values and solve for the distance.

### Example Question #1 : Using Coulomb's Law

What is the electric force between two charges, and , located apart?

Explanation:

The equation for finding the electric force between two charges is , where . Using this, we can rewrite the force equation.

Now, we can use the values given in the question to solve for the electric force between the two particles.

### Example Question #1 : Electricity And Magnetism Exam

What is the magnitude of the electric field at a field point  from a point charge of ?

Explanation:

The equation to find the strength of an electric field is .

We can use the given values to solve for the strength of the field at a distance of .

### Example Question #1 : Using Coulomb's Law

Two capacitors are in parallel, with capacitance values of  and . What is their equivalent capacitance?

Explanation:

The equivalent capacitance for capacitors in parallel is the sum of the individual capacitance values.

Using the values given in the question, we can find the equivalent capacitance.

### Example Question #161 : Ap Physics C

A proton moves in a straight line for a distance of . Along this path, the electric field is uniform with a value of . Find the force on the proton.

The charge of a proton is .

Explanation:

The force of an electric field is given by the equation , where is the charge of the particle and is the electric field strength. We can use the given values from the question to solve for the force.

### Example Question #11 : Electricity And Magnetism Exam

Two point charges,  and  are separated by a distance .

The values of the charges are:

The distance is 4.0cm. The point  lies 1.5cm away from  on a line connecting the centers of the two charges.

What is the magnitude and direction of the net electric field at point  due to the two charges?