Atoms are comprised of charges. The positively charged nucleus is attracted to the negatively charged electrons. Molecules, which are comprised of atoms, also bind together due to this charge related force of attraction. Solids and liquids, comprised of molecules, also bind together due to the electric force of charges. All forces we experience, except gravity, are due to the electric force.
Crash Crouse physics introduces us to charges.
Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.
Electric Force
To understand the effects of objects with a distribution of charges exerting a force on each other, lets start with the force between two point charges. This is known as Coulomb's Law. The below equation reads, the magnitude of the electric force of particle 2 on 1 is equal to the magnitude of the electric force of 1 on 2 (Newton's 3rd law). That force is equal to the electric constant $k$ times the magnitude of $q_1$, times the magnitude of $q_2$, divided by the absolute distance between $q_1$ and $q_2$ squared.
$|\overrightarrow{F}^E_{21}| = |\overrightarrow{F}^E_{12}| = \frac{k|q_1||q_2|}{|\Delta \overrightarrow{r}_{12}^2|}$, where $k=8.99\times 10^9 N \cdot m^2/C^2$
The direction of the net force is determined by drawing a Free-Body Diagram and using the fact that unlike charges attract and like charges repel.
This is an image of a free body diagram of the forces on an charged atom. It shows three different charges in a triangle formation with the first ion with a positive charge of four microcoulombs at seventy three degrees from the horizontal with a distance of fifteen centimeters is another ion with a charge of negative six microcoulombs. From the first ion at a distance of ten centimeters horizontally to the right is the third ion with a charge of negative five microcoulombs. To the right of this scenario is a force body diagram of the first ion showing the force vectors from the second and third ion as well as the net force vector.
Here you see an example of the FBD for $q_1$ interacting with $q_2$ and $q_3$. Since 1 is positively charged and 2 and 3 are both negatively charged, 1 is attracted to both 2 and 3. So both $F_{12}$ and $F_{13}$, acting on particle 1, are towards the other particle. The magnitude of $F_{13}$ is larger than $F_{12}$ even though $q_2$ has a greater charge. That is due to $q_3$ being closer to $q_1$ than $q_2$. With the electric force being inversely proportional to the distance between the particles and only proportional to the charge to the 1st power, being closer means a greater force in this case.
To find the force on a charged particle you typically have to do the following:
A representation with the words net charge of a system on the top. There is an equation that shows that the net charge of a system is equal to the elementary charge multiplied by the total number of protons minus the total number of electrons.
A representation with the words electric force on the top. There is an equation that shows that the magnitude of the electric force of particle two on one is equal to the magnitude of the electric force of one on two which is equal to the constant k times the magnitude of q one, times the magnitude of q two, divided by the absolute distance between q one and q two squared.
A representation with the words force on a test charge in an electric field on the top. There is an equation that shows that the force exerted on a test charge residing in an electric field is equal to the test charge multiplied by the electric field.
A representation with the words electron slash proton charge on the top. There is an equation that shows that the elementary charge of a proton is equal to positive one point six, zero, two by ten to the nineteenth power. The elementary charge of an electron is equal to negative one point six, zero, two by ten to the nineteenth power.
Now, take a look at the pre-lecture reading and videos below.
OpenStax Section 18.3 | Coulomb's Law
