Electric Charge - Online Tutor, Practice Problems & Exam Prep

Electric Charge

Hey, guys. So, I want to talk about something called electric charge in this video. You're going to need to know it for this chapter, but also for other chapters in this course. So let's get to it. But first off, I want to sort of briefly reintroduce you to an atom's and atomic structure. So remember that atoms are made of protons, neutrons, and electrons. And these protons and neutrons sit inside of this central structure in the atom that we call the nucleus. Whereas the electrons sort of float around on the outside and they orbit this nucleus. Now, there's something special about these electrons and these protons. They have a property called electric charge whereas the neutrons do not. The electric charge is a property of matter. It's just something that matter has similar to mass. So if you've seen the gravitation chapter, we can actually draw some important analogies between mass and electric charge. For instance, in gravitation, we needed mass in order to create a force. And the more mass that we had, the more gravity or the stronger that that gravitational force was. It's very similar for electric charge. You need charge in order to create an electric force, and the more charge that you have, the more or stronger that electric force becomes. Now, where things start to get a little bit different is that in mass and gravitation, we only assumed that these numbers were positive. Positive 5 kilograms, 10 kilograms, whatever. You couldn't have a negative mass. Well, physicists a couple of hundred years ago noticed that there were different interactions between charges, such that there could be positive or negative. We'll talk about that a little bit later. So, you can actually have positive and negative charges. One of the other main differences is that in mass, there was never, like, a smallest amount of mass that we could have, at least physicists that seem to think so. But in electric charges, there is something called the elementary charge. What that means is it is the smallest amount of charge that something could possibly have. And it's a letter known as e, which is \(1.6 \times 10^{-19}\), and the capital C is the unit for that which stands for coulombs. Now what I want to do is I want to make sure that you don't get confused between e and electron. So those are not the same exact thing. In fact, when we're talking about protons and electrons, we said they both have electric charge. Now, the charge of a proton is going to be positive \(e\). That's just something that we arbitrarily decided. We just decided to pick it that way, and the charge of an electron is going to be negative \(e\). So this is just sort of like the magnitude and these are actually like these signs, positive and negative. So whenever I'm referencing electrons in future videos, I'll try to do it with capital letters and I'll write something like electron just so you don't get confused between that. Okay. So we've talked about protons and electrons having charge. So now objects that are not just those things, so atoms and things like that we see every day have charge as well. And the net charge of any object is the quantity of imbalance between the number of protons and electrons inside of it. So, I want to go ahead and draw a few examples. So, we have an atom right here and all you have to do is just count up the number of protons it has. So, we got 2 protons over here, so that has plus 2 \(e\) electric charge. We also have 2 electrons on the outside. So those 2 electrons contribute negative 2 \(e\). So in other words, we have no imbalance between the protons and the electrons, so that means that the charge is just 0. That's the net charge in this object. There's no imbalance. Whereas over here, I've got 4 protons inside of the nucleus. By the way, the neutrons are also in there somewhere. I just I haven't drawn them. And, we've got plus 4 \(e\) from those elect from those protons, and we got 3 electrons on the outside. So, that's 3 electrons, 4 grand total of minus 3 \(e\). Notice how these things are not equal. There is an imbalance. In fact, this one has one more proton, so that means that the total charge is equal to plus \(e\). Now, we've got 4 electrons over here, and we've got 2 protons. So, 2 protons for a total of plus 2 \(e\), and we've got 4 electrons for a total of minus 4 \(e\). And so, it means the grand total for the imbalance is that there are 2 more electrons than protons. So that means we're going to have minus 2 \(e\). Now, I also want to point out that neutrons have zero charge. So you don't never have to worry about neutrons or anything like that. Now, I want what I also want you to recognize is in all three of these examples, these charges, the total number of charge was an entire multiple of \(e\). And there's a fancy $5 word you're going to see for that called charge quantization. And all that word means is that these things have to come in integer multiples of \(e\). You can't have half of an \(e\). You can't have negative one quarter of an \(e\). It has to be negative 1, 2, things like that. It has to be whole entire multiples. And there's an equation that we're going to be using to calculate the total charge of something. It's something that we've used in all three of these examples. Just count the number of protons and the number of electrons. You subtract them and multiply it by the elementary charge. Now, sometimes in this equation, you'll see it in your textbook with n's instead, and all that \(n\) just means is the number. So sometimes you'll see it written like this, \(n_p - n_e\). But because it has \(e\) and \(e\) here, I don't want I don't want to confuse you guys. But, that's something you definitely should be familiar with in case you see it in textbooks. Great. So, most of the materials that we're going to see in physics are going to be electrically neutral. So that means that the number of protons is perfectly equal to the number of electrons, similar to how this example actually worked out. And so the total number of the total net charge of these objects is equal to 0. So you're going to assume that objects are electrically neutral unless that problem specifically tells you that it's not. And that's it for this video, guys. Let's go ahead and take a look at some examples.

Charge of Atom

Hey, guys. Hopefully, you're able to figure this one out on your own. So in this problem, we're asked what the total charge of an atom is. We're told the amount of protons and the amount of electrons. So let's go ahead and use our charge equation. So we know that charge is equal to the number of protons minus the number of electrons, and we're going to multiply that by the elementary charge. So the total charge should be, we've got 16 protons minus 7 electrons, and that's a 7 right there. And we're going to multiply by the elementary charge, which is 1.6 times 10 to the minus 19. You're going to need to remember that number, so go ahead and commit it to memory right now.

So we've got $$\mathbin{\text{$$q = (16 - 7) \times 1.6 \times 10^{-19} $$}}= 9 \times 1.6 \times 10^{-19},$$ and that's a total charge of $$\mathbin{\text{$$1.44 \times 10^{-18}$$}}$$ coulombs. That's the total amount of charge. And what I want you to do is notice that it's also positive. And that makes sense because we have more protons; there are more protons than electrons, so we should end up with a positive number. Let me know if you guys have any questions.

How many electrons make up −1.5 × 10⁻⁵ C?

• A. 9.375×10¹³
• B. 2.4×10⁻²⁴
• C. 1.5×10¹⁴
• D. 9.375×10⁻²⁵

Electrons In Water (Using Density)

Hey, guys, let's do another example about electric charge. Okay? For starters, 1 kg per liter of water has a molecular weight of 18 g per mole and has 10 electrons per molecule.

Part A: How many electrons does two liters of water have?

Part B: What charge do these electrons represent? So, however many electrons we find in part A, what is the charge of those electrons?

For Part A, first, what we want to do is figure out how to get from liters, which is what we're given—we're given two liters of water—to the number of electrons. This will tell us how to solve the problem. We need to create a sort of map to the solution. Let's start with liters, right, because that's what's given to us. What can we go to next? Well, we're told that there's a conversion between kilograms and liters that we can say for every liter of water it has a mass of 1 kg. So we know how to go from liters to kg. Next, we have grams to moles. Now, we don't have kilograms to moles, but we know right away that 1 kg = 1000 g. So we can easily go from kilograms to grams and then using the conversion, go from grams to moles. Now, our last conversion is electrons per molecule. We don't have our number of molecules yet. We have moles, but we could use Avogadro's number to convert moles to molecules. Now, using our last conversion factor, we can go from molecules to the number of electrons. So this right here is our map. That's going to guide us through this problem.

Let's start doing these conversions. Two liters of water times 1 kg per liter equals 2 kg. So our water has a mass of 2 kg. Now right away, we know that that's equivalent to 2000 g. So we've done this step and this step. Now we need to go from grams to moles. 2000 g divided by 18 g per mole equals about 111 moles. So we've done the next step. Now we need to go from moles to molecules using Avogadro's number: 111 moles times 6 x 10²³ molecules per mole equals 6.7 x 10²⁵ molecules of water. Okay, so we've done this step. The last step is simply to figure out how many electrons are represented by this much water. As many molecules of water. We know that it's 10 electrons per molecule, so it's very simple. We just multiply this number by 10: 6.7 x 10²⁶ electrons. And we followed our map successfully from liters, which was given to us, to electrons.

Part B: What charge does this amount of electrons represent? Well, each electron has a charge of e, the elementary charge, and we have some number of electrons which we figured out in Part A. So, multiplying these together will tell us our total charge. Our number is 6.7 x 10²⁶ and the elementary charge is 1.6 x 10^-19 Coulombs. Multiplying those together we get a total charge of 1.072 x 10⁸ Coulombs.

How many electrons do you have to add to decrease the charge of an object by 16 μC?

• A. 1.0×10^-25
• B. 1.0×10¹³
• C. 1.0×10¹⁴
• D. 1.0×10¹⁷