Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons must be pres

step 1 Hello, hello, hello. We are back again with another problem. So this one states two small sphere

Two small spheres spaced 20.0 cm apart have equal charge....

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrostatic force between two charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges. This principle is fundamental in calculating interactions between charged objects.

Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charges can be positive or negative and are measured in coulombs. Understanding electric charge is crucial for analyzing interactions such as repulsion or attraction between charged particles.

Elementary Charge

The elementary charge is the smallest unit of electric charge that is considered indivisible in conventional physics. It is equivalent to the charge carried by a single proton or the negative of the charge carried by a single electron. This constant is used to quantify the amount of charge when dealing with particles like electrons.

Excess Electrons

Excess electrons refer to the additional electrons that result in a net negative charge on an object. In problems involving charged objects, calculating the number of excess electrons can help determine the net charge present, especially when the charge is quantized in terms of the elementary charge.

Transcript

00:01 Hello, hello, hello.

00:03 We are back again with another problem.

00:06 So this one states two small spheres spaced 20 centimeters apart have equal charge.

00:14 How many excess electrons must be present on each sphere if the magnitude of the force of propulsion between them is 3 .33 times 10 to the negative 21 neutrons.

00:25 So before we do anything, let's label out everything we know.

00:29 That is a very big part of physics is before you do anything, you should label what you know kind of like a map.

00:41 You want to look at your map and figure out where you're going before you head off, right? so in the same vein, we're going to write that stuff out.

00:52 So just give me this little bit of time.

00:54 So this is the force between them, the distance between them.

01:00 We're going to call r is 20 centimeters or 0 .2 meters.

01:21 And that's all they give us.

01:25 So what we're going to do is we're going to use kulom's law of forces, of electric forces.

01:34 So, kulom's law, which is spelled like this, that's an o, it's being dumb, kulom.

01:48 So, remember in that past problem where we had a charge is represented by the unit kulom, c, that's how you spell kulom right there.

01:59 Anyways.

02:01 So kulom's law, for forces specifically, states that f equals k, which is a lot, which is, which is some value or some constant that i'll bring up more elaborate or elaborate on later after i write this.

02:20 So it's kqq over r squared.

02:26 So we can kind of understand what the r part is.

02:30 It's the distance between the two charges.

02:32 Now q1 and q2 are the different charges that we're referring to.

02:38 Now the thing is, in the problem, it states that q1 is equal to q2.

02:50 They have equal amount of charge.

02:53 So in that sense, we can further simplify this to just kq squared over r squared, right? if this is two, let's say this is two.

03:09 If this is 2 and this is 2, that's 2 times 2 is 4, or alternatively, 2 squared.

03:18 Right? just math.

03:20 Nothing to be too scared of.

03:24 Anyways, so from here, we have the force.

03:28 They give it to us in the beginning, and we have the r, and k is the value that we should just know.

03:38 More specifically, i will bring that up.

03:40 K is equal to 1 over 4 pi that's a pi sorry for it being disgusting 4 pi epsilon not now what is epsilon not epsilon not if i can find it is um is the electrical constant so it's something that's always happening now it says not because it's referring to the the medium of which the electrical current is moving through.

04:18 Now if it's a different material like styrofoam or something, then this won't be e not, it'll change to a different epsilon.

04:28 So that's what epsilon refers to.

04:30 Epsilon is the material of which the electric current or the charge or whatever is passing through.

04:38 And e not or epsilon dot refers to specifically air.

04:45 Now, that is...

04:54 Shoot.

04:56 Give me a second.

05:04 I'm trying to look up the value for epsilon not, because i don't have it on me.

05:15 My computers are being slow.

05:18 Regardless.

05:19 Anyways, while that does its little thingy over there, we can continue trying to solve this.

05:25 So basically, it says the question asks, how many electrons? so that means that we'll have to be determining charges here.

05:35 So that means we're going to solve for the q.

05:38 So that means we're going to have q squared.

05:41 We're going to leave it on this side, and we're going to move everything to the force side.

05:45 So we're going to have q squared equal force times r squared all over k, where k is this, this thingy.

06:04 All right.

06:06 Epsilon not is more specifically referred to as vacuum permittivity or electric constant.

06:15 It's basically the distributed capacitance of the vacuum or the space in which the electric field is occurring in.

06:26 So for epsilon not, it is 8 .85 times 10 to the negative 12.

06:37 Ferrads per meter but i'm not going to spare you writing all that we're just going to multiply for the four pi and put it over one over and then do the reciprocal and you end up with the number hold on let me see something real quick i think i apologize the coolum's constant there we go okay so this part is 8 .85 times 10 to the negative 12 now once you plugged into the rest of this number you get 8 .9 9 times 10 to the 9th sorry that took so long i had to do the math on it real quick to make sure it came out correctly and this value this k is kulom's constant because we're referring to coolum's law coolum's equation here now the units on this constant are newtons meters squared over coolum squared now that makes sense right these these units make sense when plugged back into this because we know that q will be a coolome so if that's squared and this is in the denominator squared, those units will go away.

08:38 And meter squared and this will go away as well.

08:42 Meters squared in the numerator and this meters squared in the denominator...

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