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Chapter 6: Q12P (page 335)

Question: 鈭�V路draround the circle(x-2)2+(y-3)2=9,z=0whereV=(x2+yz2)i+(2x-y3)j

Short Answer

Expert verified

The solution is derived to bel=18蟺.

Step by step solution

01

Given Information.

The given equation is V=x2+yz2i+2x-y3j.

02

Definition of vector.

A quantity that has magnitude as well as direction is called a vector. It is typically denoted by an arrow in which the head determines the direction of the vector and the length determines it magnitude.

03

Apply Stokes’s theorem.

Apply Stokes' theorem, and the fact that鈭�脳2yzj^+-z2+2k^=2k^asz=0, andn=k^ then the solution is given below.

role="math" localid="1659262760807" l=2鈭�蟽诲蟽=2(Areaofcircle)=29蟺=18蟺

Hence, the solution is derived to be l=18蟺.

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Most popular questions from this chapter

鈭�V脳n诲蟽over the entire surface of the cube in the first octant with three faces in the three coordinate planes and the other three faces intersecting at (2,2,2), where V=(2鈭�y)i+xzj+xyzk.

鈭�V鈭�n诲蟽over the curved part of the hemisphere in Problem 24, if role="math" localid="1657355269158" V=curl(yi鈭�xj).

Find vector fieldsA such that V=curlAfor each given V.V=(y+z)i+(x鈭�z)j+x2+y2k

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