Answer:
Three linear operators A,B, and C will satisfy the condition
.
Explanation:
According to the question we have to prove.
![[[A, B],C] + [[B,C), A] + [[C, A], B] = 0](https://tex.z-dn.net/?f=%5B%5BA%2C%20B%5D%2CC%5D%20%2B%20%5B%5BB%2CC%29%2C%20A%5D%20%2B%20%5B%5BC%2C%20A%5D%2C%20B%5D%20%3D%200)
Now taking Left hand side of the equation and solve.
![[[A, B],C] + [[B,C), A] + [[C, A], B]](https://tex.z-dn.net/?f=%5B%5BA%2C%20B%5D%2CC%5D%20%2B%20%5B%5BB%2CC%29%2C%20A%5D%20%2B%20%5B%5BC%2C%20A%5D%2C%20B%5D)
Now use commutator property on it as,
![=[A,B] C-C[A,B]+[B,C]A-A[B,C]+[C,A]B-B[C,A]\\=(AB-BA)C-C(AB-BA)+(BC-CA)A-A(BC-CB)+(CA-AC)B-B(CA-AC)\\=ABC-BAC-CAB+CBA+BCA-CAB-ABC+ACB+CAB-ACB-BCA+BAC\\=0](https://tex.z-dn.net/?f=%3D%5BA%2CB%5D%20C-C%5BA%2CB%5D%2B%5BB%2CC%5DA-A%5BB%2CC%5D%2B%5BC%2CA%5DB-B%5BC%2CA%5D%5C%5C%3D%28AB-BA%29C-C%28AB-BA%29%2B%28BC-CA%29A-A%28BC-CB%29%2B%28CA-AC%29B-B%28CA-AC%29%5C%5C%3DABC-BAC-CAB%2BCBA%2BBCA-CAB-ABC%2BACB%2BCAB-ACB-BCA%2BBAC%5C%5C%3D0)
Therefore, it is proved that
.
It's pretty simple. When air is leaking out of a tire, like a tiny hole or something, the pressure in the tire decreases, because without air in the tire, there is no pressure.
Answer:
the si unit of electric current is Ampere .the flow of charge in a close circuit is called electric current
Answer:
Electric field due to two charges is given as

Explanation:
As we know that two charges are opposite in nature
So the electric field at the mid point of two charges will add together
so the net field is given as

now we have


now we have


The magnitude and direction of the electric field in the wire are mathematically given as
![L &=[(v / L) v / m] \hat{i}](https://tex.z-dn.net/?f=L%20%26%3D%5B%28v%20%2F%20L%29%20v%20%2F%20m%5D%20%5Chat%7Bi%7D)
<h3>What is the magnitude and direction of the electric field in the wire?</h3>
Generally, the equation for is mathematically given as
A cylindrical wire that is straight and parallel to the x-axis has the following dimensions: length L, diameter d, resistivity p, diameter d, potential v, and z length. combining elements from both sides
E d 
![\begin{aligned}&-E \int_0^L d x=\int_v^0 d v \\\therefore E \cdot L &=v \\L &=[(v / L) v / m] \hat{i}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26-E%20%5Cint_0%5EL%20d%20x%3D%5Cint_v%5E0%20d%20v%20%5C%5C%5Ctherefore%20E%20%5Ccdot%20L%20%26%3Dv%20%5C%5CL%20%26%3D%5B%28v%20%2F%20L%29%20v%20%2F%20m%5D%20%5Chat%7Bi%7D%5Cend%7Baligned%7D)
In conclusion, the magnitude and direction of the electric field in the wire are given as
![L &=[(v / L) v / m]](https://tex.z-dn.net/?f=L%20%26%3D%5B%28v%20%2F%20L%29%20v%20%2F%20m%5D)
Read more about electric fields
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