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Learning Goal: To review the concept of conservative forces and to understand that electrostatic forces are, in fact, conservati

CaHeK987 [17]

Explanation:

The electrostatic forces are conservative forces!

The mainly property of the conservative fields is $\vec{\nabla} \times \vec E=\vec 0$

In spherical coordinates the field's expression is:

$\vec E=\frac{Q}{4\pi \epsilon _0 r^2} .\^r$

and the curl expression is:

$\nabla\times \vec E=\frac{1}{r^2{\sin}\,\theta}\left|\begin{matrix}\hat{r} & r\,\hat{\theta} & r\,{\sin}\,\theta\,\hat{\varphi} \\& & \\\frac{\partial}{\partial r} & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial \varphi}\\ & & \\E_r & rE_\theta & r{\sin}\,\theta\, E_\varphi\end{matrix}\right|=(0, 0, 0)$

to find the expression for the potential function associated:

$\vec E=\vec \nabla . V, \Delta V= V_b-V_a=-\int _c \vec E.d\vec l=-\int _c E\^r.dr\^r=-\int _c Edr=\int \limits^a_b \frac{Q}{4\pi \epsilon _0 r^2} dr= \frac{Q}{4\pi \epsilon _0}.(\frac{1}{r}|^b_a)= \frac{Q}{4\pi \epsilon _0}.(\frac{1}{b}-\frac{1}{a})$

5 0

3 years ago

Please explain your awnser:) Thanks in advance!

podryga [215]

The skateboarder will have the greatest potential energy at point G.

Potential energy is the energy possessed by a body by virtue of its position. The gravitational potential energy of a body is given by the expression,

$E_P=mgh$

Here, m is the mass of the body, g the acceleration due to gravity and h is the height of the body from the ground.Thus as h increases, the potential energy increases.

From the figure, it can be seen that the highest point in the skateboarder's trajectory is G. hence, he would have the highest potential energy at the point G.

4 0

4 years ago

One of the most important properties of materials in many applications is strength. Two of the qualitative measures of the stren

katrin2010 [14]

To solve this exercise it is necessary to take into account the concepts related to Tensile Strength and Shear Strenght.

In Materials Mechanics, generally the bodies under certain loads are subject to both Tensile and shear strenghts.

By definition we know that the tensile strength is defined as

$\sigma = \frac{F}{A}$

Where,

$\sigma =$ Tensile strength

F = Tensile Force

A = Cross-sectional Area

In the other hand we have that the shear strength is defined as

$\sigma_y = \frac{F_y}{A}$

where,

$\sigma_y =$ Shear strength

$F_y =$ Shear Force

$A_0 =$ Parallel Area

PART A) Replacing with our values in the equation of tensile strenght, then

$311*10^6 = \frac{F}{(15*10^{-6})(30*10^{-2})}$

Resolving for F,

$F= 1399.5N$

PART B) We need here to apply the shear strength equation, then

$\sigma_y = \frac{F_y}{A}$

$210*10^6 = \frac{F_y}{15*10^{-6}30*10^{-2}}$

$F_y = 945N$

In such a way that the material is more resistant to tensile strength than shear force.

6 0

4 years ago

The electric potential at a point equidistant from two particles that have charges +Q and –Q is larger than zero. a. smaller tha

Marizza181 [45]

Answer:

idk, idk cause i'm steppin on my toes and i can't stop i make flips ou of my flops

Explanation:

8 0

4 years ago

A system is a group of parts that can be considered one unit. Storm systems, ecosystems, and our bodies are natural systems. Car

iragen [17]

The best system to talk about would be a galaxy system. Energy does not enter the galaxy, but it does "recycle" its energy. For instance, when the life of a star comes to its end, it can go super nova. and all the energy from that star is then released back into the galaxy to form nebula's and then eventually into other stars. The energy inside of a galaxy can change frequently. It can be in the form of heat from a star, or it can change into gamma radiation from an explosion. Gases like helium and hydrogen come together and form a ball of gas creating the heat. Then the heat is dispersed leaving different types of radiation like gamma, ultra-violet, microwave, and infrared. Energy can leave a system by the local black holes. Black holes with shoot out Hawking radiation is when the black hole disperses its own energy out into space, also known as Black Hole Evaporation. The energy from that black hole is then dispersed into the rest of the universe or possibly back into the galaxy from which it came from.

3 0

3 years ago

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Please Help with thia question​

Please Help with thia question