Electric Force Between Point Charges - AP Physics 2

To solve this problem, we'll need to utilize the equation for the electric force:

We're told that the force each charge experiences is 20 N at a certain distance, but then that distance is doubled. Thus, the new electric force will be:

The equation to find the force from two point charges is called Coulomb's Law.

In this equation, is force in Newtons, is the respective charge value in , is radius in meters, and is the Coulomb constant, which has a value of .

Now, we just plug in the numbers. Note: the charge values are in microcoulombs (the Greek letter , called "mu," stands for micro), which is equal to .

Therefore, the force experienced on either charge is 0.216N of force.

Use Coloumb's law:

First, convert the charges into coulombs.

Plug in values into Coulomb's law.

Negative electric forces indicate attractive forces. Alternatively, we can reason that since one charge is positive, and the other is negative, the charges will attract.

The equation for the force between two point charges is as follows:

We have the values for , , , and , so we just need to rearrange the equation to solve for , then plug in the values we have.

Therefore, the value for the second charge is .

Newton's third law states that any force interactions between two bodies must be equal. This is not so simple when another body is introduced. However, with two bodies, any force that acts on the other will have an equal and opposite reaction force.

Newton's third law states that any force interactions between two bodies must be equal. This is not so simple when another body is introduced. However, with two bodies, any force on acts on the other will have an equal and opposite reaction force. The fact that one of the bodies is moving is irrelevant when considering the relative magnitudes of the Newton's Third law pair.

Using coulombs law to solve

Where:

it the first charge, in coulombs.

is the second charge, in coulombs.

is the distance between them, in meters

is the constant of

Converting into

Plugging values into coulombs law

The magnitude will be the absolute value.

Using coulombs law to solve

Where:

it the first charge, in coulombs.

is the second charge, in coulombs.

is the distance between them, in meters

is the constant of

Converting into

Plugging values into coulombs law

Magnitude will be the absolute value

Using the electric field equation:

Where is

is charge , in

is charge , in

is the distance, in .

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Use Coulomb's law:

Where is

is charge , in Coulombs

is charge , in Coulombs

is the distance, in meters.

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Using Coulomb's law:

Where is

is charge , in Coulombs

is charge , in Coulombs

is the distance, in meters.

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Using Coulomb's law:

Where is

is charge , in Coulombs

is charge , in Coulombs

is the distance, in meters.

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Use Coulomb's law:

Where is

is charge , in

is charge , in

is the distance, in .

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Use Coulomb's law:

Where is

is charge , in

is charge , in

is the distance, in .

Convert to and plug in values:

Magnitude is equivalent to absolute value:

Use Coulombs Law:

Where

Convert to and plug in values:

k

Using Coulomb's law:

Using

Combining equations:

Converting to and to and plugging in values:

Using Coulomb's law:

Using

Combining equations:

Converting to and to and plugging in values:

Using

Plugging in values:

Using

Combining equations and plugging in values:

Solving for