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

what is biology

Hajah Reply

the study of living organisms and their interactions with one another and their environments

AI-Robot

what is biology

Victoria Reply

HOW CAN MAN ORGAN FUNCTION

Alfred Reply

the diagram of the digestive system

Assiatu Reply

allimentary cannel

Ogenrwot

How does twins formed

William Reply

They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together

Oluwatobi

what is genetics

Josephine Reply

Genetics is the study of heredity

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how does twins formed?

Misack

What is manual

Hassan Reply

discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles

Joseph Reply

what is biology

Yousuf Reply

the study of living organisms and their interactions with one another and their environment.

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discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form

Joseph Reply

what is the blood cells

Shaker Reply

list any five characteristics of the blood cells

Shaker

lack electricity and its more savely than electronic microscope because its naturally by using of light

Abdullahi Reply

advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear

Abdullahi

cell theory state that every organisms composed of one or more cell,cell is the basic unit of life

Abdullahi

is like gone fail us

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cells is the basic structure and functions of all living things

Ramadan

What is classification

ISCONT Reply

is organisms that are similar into groups called tara

Yamosa

in what situation (s) would be the use of a scanning electron microscope be ideal and why?

Kenna Reply

A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,

Hilary

cell is the building block of life.

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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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