00:01
Here i'm going to solve the problem which is shown in the screen.
00:04
I've previously submitted the solution for the same problem.
00:07
However, i made a tiny mistake when i was calculating the direction of the force.
00:14
So here i'm going to walk you through the solution again and correct the previous mistake.
00:20
So here, yeah, we have to calculate the force which is created by the electric field and which is acting on the charge two.
00:33
This force is created by two electric fields, by the electric field generated by two point charges, charge one and charge three.
00:42
So our solution of this problem will be divided into two parts.
00:46
First, we are going to refine the geometry of the system, and we are going to refine angles and distances which we need to calculate the force.
00:59
And then we will calculate the force which acts on the second charge.
01:07
Let's do the geometry part first.
01:11
So, as we know, angle 3p2 equals to angle 3p1 equals to 90 degree.
01:21
And we also know that this guy, angle 132 is a straight angle.
01:26
Distances between charges 1 and 3 and charge 3 and 2 respectively are the same and equal to a.
01:37
Therefore the angle 321 equals to the angle 312 equals to 90 degree over 2 or 45 degree.
01:53
So this angle is 45 degree.
01:59
And also the distance between charges 1 and 2 according to the pifagore theorem equals to the square root of a squared plus a squared which is a multiplied by square root of 2 okay and we've refined the geometry and now we can find the force let's redraw this system again so here our chari charges 1 3 and 2 and let's uh yeah let's repeat the signs of this charge is q1 and q2 are equal and both negative while q3 is positive, right? right.
02:46
So therefore, the first charge will act on the second charge with a repulsion force, which will be directed to the right bottom corner of the screen.
02:57
So this is f1 ,2.
02:59
And f12 is a force at which charge 1 acts on charge 2.
03:12
Charger 3 and 2 have opposite sign, therefore they will undergo attraction.
03:18
And f32 will be directed from charge 2 to charge 3.
03:23
So f32 is a force with which charge 3.
03:30
X on charge 2.
03:34
So now let's write down the equation for f2 in the vector form.
03:41
F2 vector equals to the vector sum of f1, 2 and f32 according to the superposition principle.
03:56
Now it's time to introduce the axis.
03:59
Let's direct y -axis downwards and x -axis to the x -axis to the left so now let's sketch the projection of the forces so f3 2 will be completely projected on the x -axis and it doesn't have any vertical component while f -1 -2 has both components so this is f -12 x and this is f1 2 y so as we said this guys 45 degree therefore this angle is also 45 degree because these two angles are between one line and two parallel lines.
04:50
So now let's calculate the x projection of the force acting on the second charge.
04:57
So f2x equals to f32 projected on x minus f1 ,2 projected on x.
05:06
So this guy equal, and here i want to mention again that we now we are going to use the absolute values of each component because we've already taken into account the charges.
05:20
So f32x equals to f32 and f121x equals to f121 multiplied by a cosine of 45 degree...