# 7.6 Applications of electrostatics  (Page 3/12)

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Large electrostatic precipitators    are used industrially to remove over $99%$ of the particles from stack gas emissions associated with the burning of coal and oil. Home precipitators, often in conjunction with the home heating and air conditioning system, are very effective in removing polluting particles, irritants, and allergens.

## Summary

• Electrostatics is the study of electric fields in static equilibrium.
• In addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink jet printers, and electrostatic air filters.

## Key equations

 Potential energy of a two-charge system $U\left(r\right)=k\frac{qQ}{r}$ Work done to assemble a system of charges ${W}_{12\cdots N}=\frac{k}{2}\sum _{i}^{N}\sum _{j}^{N}\frac{{q}_{i}{q}_{j}}{{r}_{ij}}\phantom{\rule{0.2em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}i\ne j$ Potential difference $\text{Δ}V=\frac{\text{Δ}U}{q}\phantom{\rule{0.2em}{0ex}}\text{or}\phantom{\rule{0.2em}{0ex}}\text{Δ}U=q\text{Δ}V$ Electric potential $V=\frac{U}{q}=-{\int }_{R}^{P}\stackrel{\to }{E}\cdot d\stackrel{\to }{l}$ Potential difference between two points $\text{Δ}{V}_{AB}={V}_{B}-{V}_{A}=\text{−}{\int }_{A}^{B}\stackrel{\to }{\text{E}}·d\stackrel{\to }{\text{l}}$ Electric potential of a point charge $V=\frac{kq}{r}$ Electric potential of a system of point charges ${V}_{P}=k\sum _{1}^{N}\frac{{q}_{i}}{{r}_{i}}$ Electric dipole moment $\stackrel{\to }{\text{p}}=q\stackrel{\to }{\text{d}}$ Electric potential due to a dipole ${V}_{P}=k\frac{\stackrel{\to }{\text{p}}·\stackrel{^}{\text{r}}}{{r}^{2}}$ Electric potential of a continuous charge distribution ${V}_{P}=k\int \frac{dq}{r}$ Electric field components ${E}_{x}=-\frac{\partial V}{\partial x},\phantom{\rule{0.2em}{0ex}}{E}_{y}=-\frac{\partial V}{\partial y},\phantom{\rule{0.2em}{0ex}}{E}_{z}=-\frac{\partial V}{\partial z}$ Del operator in Cartesian coordinates $\stackrel{\to }{\nabla }=\stackrel{^}{\text{i}}\frac{\partial }{\partial x}+\stackrel{^}{\text{j}}\frac{\partial }{\partial y}+\stackrel{^}{\text{k}}\frac{\partial }{\partial z}$ Electric field as gradient of potential $\stackrel{\to }{\text{E}}=\text{−}\stackrel{\to }{\nabla }V$ Del operator in cylindrical coordinates $\stackrel{\to }{\nabla }=\stackrel{^}{\text{r}}\frac{\partial }{\partial r}+\stackrel{^}{\mathit{\text{φ}}}\frac{1}{r}\phantom{\rule{0.2em}{0ex}}\frac{\partial }{\partial \phi }+\stackrel{^}{\text{z}}\frac{\partial }{\partial z}$ Del operator in spherical coordinates $\stackrel{\to }{\nabla }=\stackrel{^}{\text{r}}\frac{\partial }{\partial r}+\stackrel{^}{\mathit{\text{θ}}}\frac{1}{r}\phantom{\rule{0.2em}{0ex}}\frac{\partial }{\partial \theta }+\stackrel{^}{\mathit{\text{φ}}}\frac{1}{r\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\theta }\phantom{\rule{0.2em}{0ex}}\frac{\partial }{\partial \phi }$

## Conceptual questions

Why are the metal support rods for satellite network dishes generally grounded?

So that lightning striking them goes into the ground instead of the television equipment.

(a) Why are fish reasonably safe in an electrical storm? (b) Why are swimmers nonetheless ordered to get out of the water in the same circumstance?

What are the similarities and differences between the processes in a photocopier and an electrostatic precipitator?

They both make use of static electricity to stick small particles to another surface. However, the precipitator has to charge a wide variety of particles, and is not designed to make sure they land in a particular place.

About what magnitude of potential is used to charge the drum of a photocopy machine? A web search for “xerography” may be of use.

## Problems

(a) What is the electric field 5.00 m from the center of the terminal of a Van de Graaff with a 3.00-mC charge, noting that the field is equivalent to that of a point charge at the center of the terminal? (b) At this distance, what force does the field exert on a $2.00\text{-}\mu \text{C}$ charge on the Van de Graaff’s belt?

(a) What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? (b) Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.

a. $F=5.58\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\phantom{\rule{0.2em}{0ex}}\text{N/C}$ ;

The electric field is towards the surface of Earth. b. The coulomb force is much stronger than gravity.

What is differential form of Gauss's law?
help me out on this question the permittivity of diamond is 1.46*10^-10.( a)what is the dielectric of diamond (b) what its susceptibility
a body is projected vertically upward of 30kmp/h how long will it take to reach a point 0.5km bellow e point of projection
i have to say. who cares. lol. why know that t all
Jeff
is this just a chat app about the openstax book?
kya ye b.sc ka hai agar haa to konsa part
what is charge quantization
it means that the total charge of a body will always be the integral multiples of basic unit charge ( e ) q = ne n : no of electrons or protons e : basic unit charge 1e = 1.602×10^-19
Riya
is the time quantized ? how ?
Mehmet
What do you meanby the statement,"Is the time quantized"
Mayowa
Can you give an explanation.
Mayowa
there are some comment on the time -quantized..
Mehmet
time is integer of the planck time, discrete..
Mehmet
planck time is travel in planck lenght of light..
Mehmet
it's says that charges does not occur in continuous form rather they are integral multiple of the elementary charge of an electron.
Tamoghna
it is just like bohr's theory. Which was angular momentum of electron is intral multiple of h/2π
determine absolute zero
The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy
U can easily calculate work done by 2.303log(v2/v1)
Abhishek
Amount of heat added through q=ncv^delta t
Abhishek
Change in internal energy through q=Q-w
Abhishek
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
what is copper loss
this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.
Henry
it is the work done in moving a charge to a point from infinity against electric field
what is the weight of the earth in space
As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...
Prince
g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass
Jorge
Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...
Prince
Thats why it can't have a constant value of g ....
Prince
not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth
Jorge
please why is the first law of thermodynamics greater than the second
every law is important, but first law is conservation of energy, this state is the basic in physics, in this case first law is more important than other laws..
Mehmet
First Law describes o energy is changed from one form to another but not destroyed, but that second Law talk about entropy of a system increasing gradually
Mayowa
first law describes not destroyer energy to changed the form, but second law describes the fluid drection that is entropy. in this case first law is more basic accorging to me...
Mehmet
define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
explain the lack of symmetry in the field of the parallel capacitor
pls. explain the lack of symmetry in the field of the parallel capacitor
Phoebe