# 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.

why we can find a electric mirror image only in a infinite conducting....why not in finite conducting plate..?
because you can't fit the boundary conditions.
Jorge
what is the dimensions for VISCOUNSITY (U)
Branda
what is thermodynamics
the study of heat an other form of energy.
John
heat is internal kinetic energy of a body but it doesnt mean heat is energy contained in a body because heat means transfer of energy due to difference in temperature...and in thermo-dynamics we study cause, effect, application, laws, hypothesis and so on about above mentioned phenomenon in detail.
ing
It is abranch of physical chemistry which deals with the interconversion of all form of energy
Vishal
what is colamb,s law.?
it is a low studied the force between 2 charges F=q.q\r.r
Mostafa
what is the formula of del in cylindrical, polar media
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
what is flux
Total number of field lines crossing the surface area
Kamru
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
prince
what is temperature change
Celine
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
Celine
process whereby the degree of hotness of a body (or medium) changes
Salim
Q=mcΔT
Salim
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
Salim
what was the temperature of the soft drink when it was removed ?
Salim
15 degree Celsius
Celine
15 degree
Celine
ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
Salim
0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
Salim
what is d final ans for Fahrenheit and Celsius
Celine
it said what is temperature change in Fahrenheit and Celsius
Celine
the 15 is already in Celsius
Salim
So the final answer for Fahrenheit is 59
Salim
what is d final ans for Fahrenheit and Celsius
Celine
what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
Jorge
besides increasing the capacitance, is there any?
Bundi
mechanical stiffness and small size
Jorge
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
what is flux
Bundi
Bundi, flux is the number of electric field crossing a surface area
Mubanga
you right
martin,F/F=(r×r)÷(r×r)
Mostafa
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
PATRICK
somebody help me answer the question above
PATRICK
d=dQ+w
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
what are the elementary compositions of a cell?
poles, chemical
prabir
when a current pass through a material does the velocity varies
no.
prabir
what is spin entropy ?and disorder in ferromagnetic material
diagram of an hall effect sensor