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.

Part a shows the schematic of an electrostatic precipitator with four filters – initial filter, charging grid positive, charging grid negative and final filter. The photo in part b shows a power plant on a river to illustrate the effect of electrostatic precipitators. — (a) Schematic of an electrostatic precipitator. Air is passed through grids of opposite charge. The first grid charges airborne particles, while the second attracts and collects them. (b) The dramatic effect of electrostatic precipitators is seen by the absence of smoke from this power plant. (credit b: modification of work by “Cmdalgleish”/Wikimedia Commons)

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	$U (r) = k \frac{q Q}{r}$
Work done to assemble a system of charges	$W_{12 \dots N} = \frac{k}{2} \sum_{i}^{N} \sum_{j}^{N} \frac{q_{i} q_{j}}{r_{i j}} for i \neq j$
Potential difference	$Δ V = \frac{Δ U}{q} or Δ U = q Δ V$
Electric potential	$V = \frac{U}{q} = - \int_{R}^{P} \vec{E} \cdot d \vec{l}$
Potential difference between two points	$Δ V_{A B} = V_{B} - V_{A} = − \int_{A}^{B} \vec{E} \cdot d \vec{l}$
Electric potential of a point charge	$V = \frac{k q}{r}$
Electric potential of a system of point charges	$V_{P} = k \sum_{1}^{N} \frac{q_{i}}{r_{i}}$
Electric dipole moment	$\vec{p} = q \vec{d}$
Electric potential due to a dipole	$V_{P} = k \frac{\vec{p} \cdot \hat{r}}{r^{2}}$
Electric potential of a continuous charge distribution	$V_{P} = k \int \frac{d q}{r}$
Electric field components	$E_{x} = - \frac{\partial V}{\partial x}, E_{y} = - \frac{\partial V}{\partial y}, E_{z} = - \frac{\partial V}{\partial z}$
Del operator in Cartesian coordinates	$\vec{\nabla} = \hat{i} \frac{\partial}{\partial x} + \hat{j} \frac{\partial}{\partial y} + \hat{k} \frac{\partial}{\partial z}$
Electric field as gradient of potential	$\vec{E} = − \vec{\nabla} V$
Del operator in cylindrical coordinates	$\vec{\nabla} = \hat{r} \frac{\partial}{\partial r} + \hat{φ} \frac{1}{r} \frac{\partial}{\partial φ} + \hat{z} \frac{\partial}{\partial z}$
Del operator in spherical coordinates	$\vec{\nabla} = \hat{r} \frac{\partial}{\partial r} + \hat{θ} \frac{1}{r} \frac{\partial}{\partial θ} + \hat{φ} \frac{1}{r sin θ} \frac{\partial}{\partial φ}$

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.

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(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?

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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.

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

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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 $2.00 - μ C$ charge on the Van de Graaff’s belt?

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(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. $F = 5.58 \times 10^{−11} N/C$ ;

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

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Questions & Answers

how does Neisseria cause meningitis

Nyibol Reply

what is microbiologist

Muhammad Reply

what is errata

Muhammad

is the branch of biology that deals with the study of microorganisms.

Ntefuni Reply

What is microbiology

Mercy Reply

studies of microbes

Louisiaste

when we takee the specimen which lumbar,spin,

Ziyad Reply

How bacteria create energy to survive?

Muhamad Reply

Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments

_Adnan

But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?

Muhamad

they make spores

Louisiaste

what is sporadic nd endemic, epidemic

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the significance of food webs for disease transmission

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food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.

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explain assimilatory nitrate reduction

Esinniobiwa Reply

Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).

Elkana

This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products

Elkana

Examples of thermophilic organisms

Shu Reply

Give Examples of thermophilic organisms

Shu

advantages of normal Flora to the host

Micheal Reply

Prevent foreign microbes to the host

Abubakar

they provide healthier benefits to their hosts

ayesha

They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!

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what is cell

faisal Reply

cell is the smallest unit of life

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cell is the smallest unit of life

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Innocent

cell is the structural and functional unit of life

Hasan

is the fundamental units of Life

Musa

what are emergency diseases

Micheal Reply

There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️

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I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life

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Heyy Lubega hussein where are u from?

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en français

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which site have a normal flora

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Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract

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skin

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skin,Oral,Nasal,GIt

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How can Commensal can Bacteria change into pathogen?

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How can Commensal Bacteria change into pathogen?

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all

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by fussion

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what are the advantages of normal Flora to the host

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what are the ways of control and prevention of nosocomial infection in the hospital

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part of a tissue or an organ being wounded or bruised.

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what term is used to name and classify microorganisms?

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Binomial nomenclature

adeolu

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Source: OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3

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