00:01
So according to the exercise that is a charge of six couloms in an environment permeated by an electric field, a vector electric field given by this specific expression.
00:18
In terms of x, y and z, the coordinates of the location of the points in this environment.
00:30
Anyway, i presume that this a sub x, a sub y and a sub z, these are the unit vectors.
00:41
Correspondingly, i had, j had, k had of the three axes.
00:49
And okay, this charge now follows a path, starting from point m with coordinates 1 .8, 5.
01:02
I presume in meters going up to point n with a coordinate 2 .18 .6.
01:10
Again, i presume this is in meters following a line given by this expression is a typical way to express.
01:20
One of the ways we can express a line.
01:23
Yeah, for every x for a point in this line, the corresponding y is a equals 3 times x squared plus z which z is given by the expression x plus 4 in any case this is the specific line that the charge follows in this environment permeated by this rectal electric field and we want to know their work done given this path okay um the formulas that we need the formulas um the formula for the infinitesimal work infinitesimal tessimal work is just yeah all we have to do is take the force accepted on the on the on the on the on the on the body in this case on the charge the electric force except on the charge and dot it with d l the infinitesimal um yeah the infinitesimal path let's say the infinitesimal um displacement of the charge anyway f -electric typically equals just the product of the charge times the electric field.
02:48
So basically, okay, this is the expression that we need for the infinitesimal work.
02:57
In order to get the finite work, the total work.
03:01
Supposedly all we have to do is perform the line integral, line integral.
03:06
Over the path we've been given.
03:09
This is quite compass.
03:10
This is this is yeah it's doable but it takes quite some time to do this.
03:20
A faster way to do this is the following...