Three charges, q1=+q, q2=-q, and q3=+q, are at the vertices...

Three charges, $q_{1}=+q, q_{2}=-q,$ and $q_{3}=+q,$ are at the vertices of an equilateral triangle, as shown in Figure $19-31$. (a) Rank the three charges in order of increasing magnitude of the electric force they experience. Indicate ties where appropriate. (b) Give the direction angle, $\theta$, of the net electric force experienced by charge $1 .$ Note that $\theta$ is measured counterclockwise from the positive $x$ axis. (c) Repeat part (b) for charge 2 . (d) Repeat part (b) for charge 3 .

Transcript

00:01 Hello everyone, so let's take a look at the question and the question says that three charges q1, okay, given are three charges q1 is equal to positive q, q2 is equal to negative q and q3 is equal to positive q are at the vertices of an equilateral triangle, okay.

00:32 So, first in the question we have to do is rank the three charges in order of increasing magnitude of the electric force, the experience and indicate ties with where appropriate, okay.

00:47 So, next in the question give the direction angle theta of the net electric charge, net electric force experienced by the charge and the third is repeat part b for charge two and repeat part b for charge three, right.

01:09 So, here the question you've got, now let's take a look at the solution.

01:17 So, now let d be the distance between each charge and the force q1 is f1, force on q2 is f2 and force on q3 is f3, alright.

02:05 Now, let f be the magnitude, magnitude of the force between two charges, alright.

02:26 So, f that we get is 1 divided by 4 pi epsilon naught into q square by d square, alright.

02:43 So, now let's look further into the solution on q1 the force that would be acting that is f1 is equal to under the root f square plus f square plus 2f square cos 120 degree, alright.

03:13 So, when we solve this further we get f square plus f square plus 2f square into 1 by 2 that is the value of cos 120, alright.

03:30 So, when we solve this further we get f square plus f square minus f square, alright.

03:40 So, the final answer that we get is f over d.

03:44 So, now we repeat the same process on q2 that is f2 is equal to f square plus f square plus 2f square plus cos 60 degree, alright.

04:05 So, this when we solve further we get f square plus f square plus 2f square into 1 by 2, alright.

04:24 So, here f square under the root f square plus f square plus f square that gives us under the root 3f, okay.

04:39 So, now the same process we do for q3.

04:46 So, here i will write q3 is answered directly f3 is equal to under the root f square plus f square plus 2f square cos 120, alright.

05:07 So, the answer comes up to f.

05:11 So, therefore force on q1 is equal to force on q3 and less than force on q2, alright.

05:36 So, mathematically we write it as f1 is equal to f3 is greater than f2, is smaller than f2, alright.

05:48 So, f2 is greater.

05:51 Now, let us take a look at the next part of the solution.

05:55 So, now we will draw a diagram of where charge q1 is placed, alright...

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