Chapter 16.2, Problem 42E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The force exerted by an electric charge at the origin on a charged particle at a point (*x*, *y*, z) with position vector **r** = `⟨`

*x*, y, *z*`⟩`

is **F**(**r**) = *K***r**/|** r** |^{3} where *K* is a constant. (See Example 16.1.5.) Find the work done as the particle moves along a straight line from (2, 0, 0) to (2, 1, 5).

To determine

**To find:** The work done by the particle when it moves along a straight line from the point

Explanation

**Given:**

The force field is

The position vector is

The particle moves along a straight line from the point

**Formula used:**

The work done by the force field

Where,

The parametric equations for a line segment through the point

The director vector

To calculate the vector

Substitute 2 for

Consider the limits of scalar parameter

Write the position vector from the parametric equations as follows.

Write the equation of force field as follows.

Substitute the position vector

To find the derivative of the vector function, differentiate each component of the vector function.

Differentiate each component of the vector function

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