The first law is about force or push and pull
Answer:
The curl is ![0 \hat x -z^2 \hat y -4xy \hat z](https://tex.z-dn.net/?f=0%20%5Chat%20x%20-z%5E2%20%5Chat%20y%20-4xy%20%5Chat%20z)
Explanation:
Given the vector function
![\vec A (\vec r) =4x^3 \hat{x}-2x^2y \hat y+xz^2 \hat z](https://tex.z-dn.net/?f=%5Cvec%20A%20%28%5Cvec%20r%29%20%3D4x%5E3%20%5Chat%7Bx%7D-2x%5E2y%20%5Chat%20y%2Bxz%5E2%20%5Chat%20z)
We can calculate the curl using the definition
![\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\A_x&X_y&A_z\end{array}\right|](https://tex.z-dn.net/?f=%5Cnabla%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%20x%26%5Chat%20y%26%5Chat%20z%5C%5C%5Cpartial%2F%5Cpartial%20x%26%5Cpartial%2F%5Cpartial%20y%26%5Cpartial%2F%5Cpartial%20z%5C%5CA_x%26X_y%26A_z%5Cend%7Barray%7D%5Cright%7C)
Thus for the exercise we will have
![\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\4x^3&-2x^2y&xz^2\end{array}\right|](https://tex.z-dn.net/?f=%5Cnabla%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%20x%26%5Chat%20y%26%5Chat%20z%5C%5C%5Cpartial%2F%5Cpartial%20x%26%5Cpartial%2F%5Cpartial%20y%26%5Cpartial%2F%5Cpartial%20z%5C%5C4x%5E3%26-2x%5E2y%26xz%5E2%5Cend%7Barray%7D%5Cright%7C)
So we will get
![\nabla \times \vec A (\vec r )= \left( \cfrac{\partial}{\partial y}(xz^2)-\cfrac{\partial}{\partial z}(-2x^2y)\right) \hat x - \left(\cfrac{\partial}{\partial x}(xz^2)-\cfrac{\partial}{\partial z}(4x^3) \right) \hat y + \left(\cfrac{\partial}{\partial x}(-2x^2y)-\cfrac{\partial}{\partial y}(4x^3) \right) \hat z](https://tex.z-dn.net/?f=%5Cnabla%20%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%3D%20%5Cleft%28%20%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%28xz%5E2%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%28-2x%5E2y%29%5Cright%29%20%5Chat%20x%20-%20%5Cleft%28%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%28xz%5E2%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20z%7D%284x%5E3%29%20%5Cright%29%20%5Chat%20y%20%2B%20%5Cleft%28%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20x%7D%28-2x%5E2y%29-%5Ccfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%284x%5E3%29%20%5Cright%29%20%5Chat%20z)
Working with the partial derivatives we get the curl
![\nabla \times \vec A (\vec r )=0 \hat x -z^2 \hat y -4xy \hat z](https://tex.z-dn.net/?f=%5Cnabla%20%20%5Ctimes%20%5Cvec%20A%20%28%5Cvec%20r%20%29%3D0%20%5Chat%20x%20-z%5E2%20%5Chat%20y%20-4xy%20%5Chat%20z)
Answer:
relates the electric field at points on a closed surface to the net charge enclosed by that surface.
Explanation:
Gauss Law states that overall electric flux of a closed surface is equivalent right to charge enclosed which is divided by the permittivity. In other words Gauss Law stress that
net electric flux that pass through an hypothetical closed surface is equivalent to overall electric charge present within that closed surface.
The Gauss law can be expressed mathematically as
ϕ = (Q/ϵ0)
Q = total charge within the surface,
ε0 = the electric constant
Answer:
1) The human skeleton performs six major functions: support, movement, protection, production of blood cells, storage of minerals, and endocrine regulation. protection of internal organs
2) Joints are where two bones meet. They make the skeleton flexible — without them, movement would be impossible. Joints allow our bodies to move in many ways.
3)A joint is a point where two or more bones meet. There are three main types of joints; Fibrous (immovable), Cartilaginous (partially moveable) and the Synovial (freely moveable) joint
4)A ligament is a fibrous connective tissue which attaches bone to bone, and usually serves to hold structures together and keep them stable.
Explanation:
go-gle your welcome ;)
Answer: Kinetic Molecular Theory claims that gas particles are in continuous motion and completely demonstrate elastic collisions. Kinetic Molecular Theory can be used to describe the rules of both Charles and Boyle. A series of gas particles only has an average kinetic energy that is directly proportional to absolute temperature.