Vector Calculus

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

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### Video Transcript

we don t r sequence are asked to show So wt to show that is equal. No, I divided by two All right on were also given that c is X squared plus y sprayer. And then what we do her amateur isa circle. We just set X equal to Broncos 90 and lies our site. And then So we want to change everything's of the integral along. See, if be not your we want to write everything in terms. Okay, so we take the derivative of far churches are running. And that way, get a derivative or co scientist, negative or scientist and the derivative of bar scientist, he's Park Coast. All right, so now what? We have to determine this big B or the magnetic. Well, we have to think about this for a little bit. So what? We know this is that the magnetic field it's gonna be Terran Jim to the to the curve. See? So basically, what we have is a wire. Then we have a plane, and we have circles are on this plane that we know that magnetic field be just like our primes. So that means being is going to be of the same four as our friends are. So our our our prime was negative for society and a comma Arco site. So since both are right and the are gonna be tension to the curb seat or the circle, it's going to be of the same form. So obvious. Negative sign T and a comma. Bi coastal. Thanks, but no, we put everything in, so we're gonna plug him. So now we're gonna plug into integral mercy of the adult. Uh, sorry. Uh, yeah. See, you need us. We are, and then we're gonna rewrite it Now, in terms of teeth, that's gonna be the integral from 0 to 2 pi from the our pride. All right, so he has just negative be scientific common close eye teeth and our our primes gonna be our sign T I'm sorry. Negative. Our society comma Arcos in and we take the dot product. So we get it's bor Stein Spirit t plus beyond concise for TV tea. We can take her. The Byars, the common factor. What we're left with is signed spire teeth. Bus goes for team, which is one so are integral. No, it's greatly simplify. We have the integral from 0 to 2 pi off the rt and remember the limit Its plus 0 to 5 because our all right, so now be in order constants but convicted outside. And that the integral bt's Justine and it goes from 0 to 2 pi. So then you're gonna take the difference which is to 50 or to find Czar so are integral. Whoever c a b dot br is just to buy And then we're given in the question that this integral dizzy Putin would not see. So now if we try to solve for the weekend, we're gonna have to divide by two pi r on both sides. So we get finally that be it's you not I divided like to buy on This is exactly what we wanted to show So we're don't with a verification

#### Topics

Vector Calculus

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp