Question

The force in an electrostatic field given by f(x, y, z) has the direction of the gradient. Find ∇f and its value at P.

Solutions

Verified
Step 1
1 of 2

The gradient of a function is defined as

=xi+yj=(x,y)\nabla=\frac{\partial}{\partial x}\textbf{i}+\frac{\partial}{\partial y}\textbf{j}= \Big(\frac{\partial}{\partial x},\frac{\partial}{\partial y}\Big)

Let's find partial derivates.

x=yy=x\begin{align*} \frac{\partial}{\partial x} &= y\\ \frac{\partial}{\partial y} &=x \end{align*}

Consequently,

f=(x,y)=(y,x)\boxed{ \nabla f=\Big(\frac{\partial}{\partial x},\frac{\partial}{\partial y}\Big)=(y, x)}

Since p=(4,5)p=(-4,5) we have:

f(p)=(5,4)\color{#c34632}{ \nabla f (p)= (5,-4)}

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Recommended textbook solutions

Advanced Engineering Mathematics 10th Edition by Erwin Kreyszig

Advanced Engineering Mathematics

10th EditionISBN: 9780470458365 (8 more)Erwin Kreyszig
4,134 solutions
Advanced Engineering Mathematics 9th Edition by Erwin Kreyszig

Advanced Engineering Mathematics

9th EditionISBN: 9780471488859 (2 more)Erwin Kreyszig
4,201 solutions
Advanced Engineering Mathematics 7th Edition by Peter V. O'Neil

Advanced Engineering Mathematics

7th EditionISBN: 9781111427412 (1 more)Peter V. O'Neil
1,608 solutions
Advanced Engineering Mathematics 6th Edition by Dennis G. Zill

Advanced Engineering Mathematics

6th EditionISBN: 9781284105902 (2 more)Dennis G. Zill
5,281 solutions

More related questions