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Chapter 14: Q 3 (page 1153)

Find a potential function for the vector field

G(x,y,z)=x2e51+2xyze5j+xe5k

Short Answer

Expert verified

The potential function is

Step by step solution

01

Step 1:Given information 

The given expression isG(x,y,z)=x2e51+2xyze5j+xe5k

02

Step 2:Simplification 

Consider the vector field

G(x,y,z)=x2e51+2xyze5j+xe5k

To find potential function

G(x,y,z)=鈭�g(x,y,z)

=鈭�g鈭�xi+鈭�g鈭�yj+鈭�g鈭�zk

here

鈭�g鈭�x=gx=zey2

鈭�g鈭�y=gy=2xyzey2

鈭�g鈭�z=gz=xey2

integrate gxw.r.t x

g(x,y,z)=xzey2+B(y).... equation (1)

here B is constant

Then differentiatingg(x,y,z)w.r.t y

gy(x,y,z)=2xyzey2+B'(y)

Comparingthis withgy=2xyzey2

B'(y)=0

Integratingthis with respect toy,

Thus,B(y)=0+h(z)

Now substitute this value in (1)

g(x,y,z)=xzey2+h(z)鈥�鈥�(2)

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Most popular questions from this chapter

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