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) = kr/|r|3 where k is a constant. find the work done as the particle moves along a straight line from (4, 0, 0) to (4, 3, 4).

Step-by-step explanation:

The straight line path between point (a,b,c) and (l,m,n) is parametric by the expression

since we are giving point (4,0,0) and (4,3,4), the parametric equation is giving below

using the dot product system of multiplication, we have

t is between 0,1.

Next we define the line integral for work done which is express as

First we define the general expression for the force

If we substitute our parametric equation we arrive at

also we need to find the expression for dr

Now we substitute into the integral expression

using dot product we arrive at

let make a simple substitution so we can simplify the integral,

let assume

and changing setting the new upper and lower limit, we have

by simple integral we arrive at

Hence the workdone is

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