Problem

Point charges of 5.00$\mu \mathrm{C}$ and $-3.00 …

Problem 38 Hard Difficulty

(a) Two point charges totaling 8.00$\mu C$ exert a repulsive force of 0.150 $\mathrm{N}$ on one another when separated by 0.500 $\mathrm{m}$ . What is the charge on each? (b) What is the charge on each if the force is attractive?

Answer

a)
$q_{1}=7.44 \mu \mathrm{C}, \quad q_{2}=0.56 \mu \mathrm{C}$
b)
$q_{1}=8.49 \mu \mathrm{C}, \quad q_{2}=-0.49 \mu \mathrm{C}$

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Physics 102 Electricity and Magnetism

College Physics for AP® Courses

Chapter 18

Electric Charge and Electric Field

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Video Transcript

in this case, we are given the information that two charges queue and queue to add up to eight micro cooler. Also, the force is given as 0.15 Newton. From that information, we can find that one divided by four pi upsilon, not science. Q. One Q two, divided by Mr Square, is equal to 1.0 point 15 Now this information here is enough to find us the product off Cuban and few, too, which is here. So the products of Cuban and que tu is given by from the from this year, you can see that this factor here is going to divide on the right inside, and the factor of our square is going to multiply on right inside. So 0.15 our square is 0.5 square. Since the distance is given his 0.5 on the factory off one divided by one by four. Perhaps there are not. It's nine times 10 power night. This gives us the value 4.2 times 10 power negative. 12. So let's ride down in a way that it is simplified. So Cuban que tu is equal to 4.2 micro Coolum squared. This is what we expect because this is a product off two charges which are off the order off my pro Coolum. So it should be micro colon squared and 10 power to 12 is the factor which conform Stack. Now let's substitute Kyu won in terms off you two. So Cuban is it will do h minus you, too. So eight minus Q to science, you too, is equal to 4.2. So this gives us the question. What radically question? Which is cute too square minus eight. Q. Two plus 4.2 is equal to zero. You can solve this quadratic equation by the solution of quality question, which is given by Que Tu is equal to negative. Oh, this factor here, which is negative. Eight. Yes, minus square Root Oh, eight squared. Actually, it's negative. It's square, but it's going to be positive minus four times. The factor here is one, and factor here is 4.2, divided by twice the factor again. Here it's one. So let's all that square root off 64 minus a point 16.8 is given by 6.87 so we have two solutions here you two, equal to positive ate less, minus six point 87 divided by two. So one solution will be 56 and another solution will be 7.4 three. Fight. So what solution do we keep? We can keep both. Since I said for 0.56 I should right here from 56 not find five, too, so we can keep the boat solutions because you can check that 0.56 plus 7.435 If you add 0.56 to 7.435 you get the value. Eight. This means that these two solutions are complimentary. So if you two has a value off 0.56 Q one from here, we'll have the value. Eight minus Q two, which is 7.43 Bite similar leave. Q two Takes the value off 7.435 Q one takes the value off 10.56 All the values are in micro cooler now. Next task is to find out with same charges if the force was attractive instead of being repulsive. So we use the force isn't well 2.15 which is positive now it is negative. In part be so Cuban que tu. We'll have the Negative Valley here, which was 4.2 micro problem Square. We would have negative 4.2 Michael Pollan Square. So that changes the solution because we will have the change in here. Secure to is equal to everything will remain the same except the factor of four point to here shall have negative sign so it will affect the value here. No, you too is equal to How's it to age? Less minus square root off a square, which is 64. So instead of having negative sign, we will have positive sign or let me write it down for this step as negative 4.2 divided by two. So let's all this 64 plus four times 4.2 is 16.8, which is 80.8. And if you take the square root off this value, we will get the value as 8.988 divided by two. No, it means that you two can have two separate values. One value will be negative. 10.9 88 divided by two or another value will be 16.9 88 divided by two. See that one values positive and one values negative. In this case, you'll get the answer as here it's eight point five. Michael, will you? Oh, it's this is just one divided by two. Let's approximately 2.5. Michael. Hello. So if you again, are these two charges 8.5 and negative 0.5, they will get eight. That means these two values are complimentary. So if you two takes the value of negative 20.5 Q one will take the valley off positive. 8.5 micro cooler. Similarly, if you to text of Ali off a point like you want shall take the value off negative 0.0.5. Micropal, You can do this calculation more accurately to see that this value here is actually negative 0.49 and this value here is actually positive. 8.49 I decided not if question quadratic equation is given us a X squared plus, BX plus C is equal to zero. The solution to this equation is negatively plus minus square root B squared minus four. Is he divided by twice? A. This is what I have used to find the solution in the parts A and

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