View by Category

Loading...

PPT – Electrostatic Fields: PowerPoint presentation | free to view - id: 273d8a-ZWI3N

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

CHAPTER 2

ELECTROMAGNETIC FIELDS THEORY

- Electrostatic Fields
- Electric flux and electric flux density
- Gauss's law

In this chapter you will learn

- Electrostatic Fields
- -Charge, charge density
- -Coulomb's law
- -Electric field intensity
- - Electric flux and electric flux density
- -Gauss's law
- -Divergence and Divergence Theorem
- -Energy exchange, Potential difference, gradient
- -Ohm's law
- -Conductor, resistance, dielectric and

capacitance - - Uniqueness theorem, solution of Laplace and

Poisson equation

Electric Potential

- Another way of obtaining E, besides Coulombs law

and Gausss law is using electric scalar

potential, V

Electric Potential

In moving the object from point A to B, the work

can be expressed by

dL is differential length vector along some

portion of the path between A and B

Electric Potential

The work done by the field in moving a charge

from A to B is

If an external force moves the charge against the

field, the work done is negative

Electric Potential

- The work done by an external agent to move a

point charge Q from A to B in an electrical field

E is - Total work done (or potential energy)

Negative sign indicates that the work is done by

an external agent

Electric Potential

- Divide W by Q, we get the electric potential

energy per unit charge or potential difference

between points A and B - A is initial point while B is the final point
- In other word, to find the potential difference

between two points, we must integrate Edl along

the path between point A to point B.

The work done per unit charge by an external

agent to transfer a test charge from infinity to

that particular point

Electric Potential (due to point charge)

- E field due to a point Q at origin is
- So VAB is

Electric Potential

- Or we can write VAB as
- Where VA and VB are the potentials (or absolute

potentials) at B and A, respectively. VA is

potential at B with reference to A. - For point charge, choose reference point at

infinity. - rA ? 8 VA 0, then the potential at any point

(rB ?r) due to point charge Q at origin is

Electric Potential

- E points in radial direction ? displacement in

the ? or F direction is wiped out by the dot

product. - Thus VAB is independent of the path taken.

Electric Potential

- If point charge Q is not located at origin, but

at another point with position vector r, thus

V(x, y, z) or simply V(r) at r becomes - For more than one point charges, the

superposition principle applies

Electric Potential

- For continuous charge distributions

Electric Potential

- If another point is chosen as a reference instead

of infinity, V becomes - where C is a constant that is determined at the

chosen point of reference. - The potential difference VAB can be written as

Example

- Two point charges, -4 µC and 5 µC are located at

(2,-1,3) and (0, 4, -2) respectively. Find

the potential at (1, 0, 1) assuming zero

potential at infinity.

Solution

- Let

2nd Maxwell Equation

- Potential difference is independent of path

taken. - So VBA - VAB
- That is
- Or
- The line integral of E along a closed path must

be zero. - No net work is done when moving a charge along a

closed path in an electrostatic field

2nd Maxwell Equation

- Applying Stokes theorem, becomes
- The field E is conservative, or irrotational

2nd Maxwell Equation

Relationship between E and V

- We know that
- But
- Compare (1) and (2), we get

Relationship between E and V

- Thus

Electric field intensity, E is the gradient of V

with opposite direction of increasing V

Example

- Given the potential
- Find the electric flux density D at (2, p/2, 0)
- Calculate the work done in moving a 10µC charge

from point A (1,30,120) to B(4,90,60)

Solution

- (a)
- But
- at point (2, p/2, 0)

Solution

- (b) The work done can be found using either E or

V

(No Transcript)

(No Transcript)

Energy Density in Electrostatic Field

- The total work done in positioning the three

charges

Energy Density in Electrostatic Field

- Lets say the order is reversed, thus

Energy Density in Electrostatic Field

Energy Density in Electrostatic Field

- So we can say

The unit for W is joules

Energy Density in Electrostatic Field

Energy Density in Electrostatic Field

- Thus we can apply the identities and get
- Apply divergence theorem on the first term on the

right-hand side of this equation, we get

Energy Density in Electrostatic Field

- The first integral tends to zero an the surface S

becomes large. Thus, the equation is reduced to

Energy Density in Electrostatic Field

- So the electrostatic energy density can be

defined as

Example

- Three point charges -1 nC, 4 nC, and 3 nC are

located at (0,0,0), (0,0,1) and (1,0,0)

respectively. Find the energy in the system

Solution

(No Transcript)

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Electrostatic Fields:" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Ump University and other schools with their online training by sharing educational presentations for free