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

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.

Kate Reply

To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.

Muhammed

What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?

Kate Reply

what is the change in momentum of a body?

Eunice Reply

what is a capacitor?

Raymond Reply

Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.

Gautam

A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate

Maria Reply

please solve

Sharon

8m/s²

Aishat

What is Thermodynamics

Muordit

velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.

Mehmet

A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat

Saheed Reply

50 m/s due south east

Someone

which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer

Ramon Reply

I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.

Someone

Scratch that

Someone

temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....

Someone

about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle

Someone

definitely of physics

Haryormhidey Reply

how many start and codon

Esrael Reply

what is field

Felix Reply

physics, biology and chemistry this is my Field

ALIYU

field is a region of space under the influence of some physical properties

Collete

what is ogarnic chemistry

WISDOM Reply

determine the slope giving that 3y+ 2x-14=0

WISDOM

Another formula for Acceleration

Belty Reply

a=v/t. a=f/m a

IHUMA

innocent

Adah

pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?

Nassze Reply

how do lnternal energy measures

Esrael

Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.

JALLAH Reply

No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.

Dlovan

Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?

Robert

like charges repel while unlike charges atttact

Raymond

What is specific heat capacity

Destiny Reply

Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).

AI-Robot

specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin

ROKEEB

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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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