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Two charges Q and 5Q, are separated by some distance. How do the forces compare on each charge? Why?
What is the electric force between charges of +4.5 x 10-6 C and +7.2 x 10-6 C when they are separated by a distance of 0.30 cm? Is it attractive or repulsive?
A hydrogen atom is made up of 1 proton and 1 electron separated by a distance of 5.3x10−11m. How does the electric force compare to the gravitational force between these particles?

1) No

2) Yes

3) No

4) Equal and opposite

5) 32400 N

6) Repulsive

7) The electric force is times bigger than the gravitational force

Explanation:

1)

In nature, the minimum possible charge that an object can have is the charge of the electron, which is called fundamental charge:

Electrons are indivisible particles (they cannot be separated), this means that an object can have at least the charge equal to the charge of one electron (in fact, it cannot have a charge less than , because it would meant that the object has a "fractional number" of electrons).

In this problem, the object has a charge of

If we compare this value to , we notice that , so no object can have a charge of .

2)

As we said in part 1), an object should have an integer number of electrons in order to be charged.

This means that the charge of an object must be an integer multiple of the fundamental charge, so we can write it as:

where

Q is the charge of the object

n is an integer multiple

e is the fundamental charge

Here we have

Substituting the value of e, we find n:

n is integer, so this value of the charge is possible.

3)

We now do the same procedure for the new object in this part, which has a charge of

Again, the charge on this object can be written as

where

n is the number of electrons in the object

Using the value of the fundamental charge,

We find:

n is not integer, so this value of charge is not possible, since an object cannot have a fractional number of electrons.

4)

To solve this part, we use Newton's third law of motion, which states that:

"When an object A exerts a force on an object B (Action force), then object B exerts an equal and opposite force on object A (reaction force)".

In this problem, we have two objects:

- A charge Q

- A charge 5Q

Charge Q exerts an electric force on charge 5Q, and we can call this action force. At the same time, charge 5Q exerts an electric force on charge Q (reaction force), and according to Newton's 3rd law, the two forces are equal and opposite.

5)

The magnitude of the electric force between two single-point charges is

where

k is the Coulomb's constant

q1, q2 are the two charges

r is the separation between the two charges

In this problem we have:

is charge 1

is charge 2

r = 0.30 cm = 0.003 m is the separation

So, the electric force  between the two charges is

6)

The electric force between two charged objects has direction as follows:

- If the two objects have charges of opposite signs (+ and -), the force between them is attractive

- If the two objects have charges of same sign (++ or --), the force between them is repulsive

In this problem, the two charges are:

is charge 1

is charge 2

We see that the two charges have same sign: therefore, the force between them is repulsive.

7)

The electric force between the proton and the electron in the atom can be written as

where

is the magnitude of the charge of the proton and of the electron

is the separation between them

So the force can be rewritten as

The gravitational force between the proton and the electron can be written as

where

G is the gravitational constant

is the proton mass

is the electron mass

Comparing the 2 forces,