Chapter 16.3, Problem 23E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the work done by the force field **F** in moving an object from *P* to *Q*.

**23. F**(*x*, *y*) = *x*^{3} **i** + *y*^{3} **j**; *P*(1, 0), *Q*(2, 2)

To determine

**To find**: The work done by force field

Explanation

**Given data:**

Force field is

**Formula used:**

Consider a vector field as

Here,

*P*, and

*Q*,

Write the expression for work done

Here,

*f* is potential function of

Consider vector function
*C*. Consider *f* is a differentiable function two or three variables of gradient function
*C*. Then,

Compare the force field

Apply partial differentiation with respect to *y* on both sides of equation (4).

Apply partial differentiation with respect to *x* on both sides of equation (5).

Substitute 0 for

Therefore, force field
*f* such that

Consider

Write the relation between the potential function *f* and vector field

Substitute

Compare the equation

Compare the equation

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