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Chapter 6: Q14P (page 335)

鈭�(yi鈭�xj+zk)鈭�draround the circumference of the circle of radius 2, center at the origin, in the (x,y)plane.

Short Answer

Expert verified

The solution derived isI=-8蟺.

Step by step solution

01

Given Information.

The given expression is鈭�(yi鈭�xj+zk)鈭�dr

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 its magnitude.

03

Apply Stokes’s theorem.

Apply Stokes' theorem and the fact that 鈭�脳V=鈭�2k^,Z=0and then the question can be solved as shown below.

I=鈭�2鈭�蟽鈥�诲蟽

=2(Area of circle)

=-2(4)蟺

=-8蟺

Hence, the solution derived is I=-8蟺.

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Most popular questions from this chapter

If A and B are unit vectors with an angle 胃 between them, and is a unit vector perpendicular to both A and B , evaluate [A脳B脳B脳C脳C脳A]

Write out the equations corresponding to (9.3) and (9.4) for Q=2Xbetween points 3 and 4 in Figure 9.2, and add them to get (9.6).

鈭�鈥�curlV)脳nd蟽over any surface whose bounding curve is in the (x,y)plane, where V=(x鈭�x2z)i+(yz3鈭�y2)j+(x2y鈭�xz)k.

Evaluate the line integral 鈭�xydx+xdyfrom(0,0)to(1,2) along the paths shown in the sketch.

Given

F1=2xzi+yj+x2kF2=yi-xj:

(a) Which F , if either, is conservative?

(b) If one of the given 鈥檚 is conservative, find a function Wso that F=鈭�W.

(c) If one of the F鈥檚 is non conservative, use it to evaluate 鈭�F along the straight line from (0,1)to(1,0).

(d) Do part (c) by applying Green鈥檚 theorem to the triangle with vertices (0,0),(0,1),(1,0).(0,0),(0,1),(1,0)..
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