(a) At room temperature, what is the strength of the electric field in a 12 gauge copper wire (d

step 1 Okay, Hopefully, this is a recording. So to approach this problem s o let me just read it again

(a) At room temperature, what is the strength of the...

Key Concepts

Electric Field

The electric field in a conductor is the force per unit charge that drives the current. It is directly linked to the drift velocity of charge carriers and is established when a potential difference is applied across the conductor. In many situations involving metals, the electric field can be related to the current density and resistivity by the relation E = ?J.

Current Density

Current density is the amount of electrical current flowing per unit cross-sectional area of a conductor. It is a key concept in understanding how electric fields drive current in conductive materials. The higher the current density, the larger the electric field needed to overcome the material's inherent resistance to the flow of electrons.

Resistivity

Resistivity is a material-specific property that quantifies how strongly a material opposes the flow of electric current. It plays a critical role in determining the electric field required for a given current density in a conductor. Materials with lower resistivity require a weaker electric field to maintain the same current compared to materials with higher resistivity.

Transcript

00:05 Okay, hopefully, this is a recording.

00:11 So to approach this problem s o let me just read it again at room temperature.

00:21 What is the strength of the electric field and a twelve gauge copper riot wire with a given diameter that is needed to cause a particular current to flow.

00:29 So we want to look through the formula that release these quantities.

00:35 And that formula is given by me.

00:41 Equals the reason stimpy of the material, which is thiss given red symbol rose so well, fine.

00:48 Look up the road for copper time's a current density, and that current density is thie current per unit area flowing through the wire.

00:59 So, like, this is the wire.

01:05 Um, will has some area a it's the current for unit cross sectional area.

01:16 Um, so you can look out of the book that the resistive iti what city was a copper? um, yeah, copper.

01:27 You can look up that the resistive ity of proper is oh, let's see, point me use double check this.

01:45 Um, so i'm just gonna look at the example that they do in the book.

01:49 It's really similar.

01:50 And that's example.

01:51 Twenty five point to, um and for copper.

01:57 And that example in one point seven two times ten to the minus a o meter.

02:04 And so let me see where they get five to be.

02:07 Table twenty five one one.

02:08 Okay, there it is.

02:10 So yeah.

02:12 So then we know that row is one point seven two times ten to the minus e.

02:28 And then the current density is going to be given by the client that we want.

02:34 So that's four and a half.

02:40 And then the cross sectional area is just going to be so the formula for class sectional area is going to be pi times the radius of this process.

02:50 Small area so far.

02:55 See? okay, i'll actually let me just computed on the side, so it's going to be a pi times d over to swearing.

03:09 Uh, i'll, uh make sure to convert that sa units put money before these little units on my row while i see that.

03:17 Okay, back to the area.

03:19 So the diameters two point five millimeters.

03:22 So then the radios is half of that, which is one point o two five millimeters.

03:33 So one point oh, two, five.

03:39 It was time to minus, i swear, and yeah, so i'm just gonna leave it like that and then fried it over here.

03:55 So that's high times one point oh, two five.

04:01 And i thought if i said that, but you need to convert it to meters to keep all these and s i s units.

04:06 So your electric field, it's because the s i unit of who loans on then you kind of just take this.

04:16 Okay, so now we have the full expression for you after killed your community.

04:24 And if you plug that into repopulate, er, um, go ahead and do that...

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