Download presentation

Presentation is loading. Please wait.

Published byNatalie Pearson Modified over 3 years ago

1
The divergence of E If the charge fills a volume, with charge per unit volume . R Where d is an element of volume. For a volume charge:

2
Thus: Gauss’s law in differential form.

3
**Spherical polar coordinates (r, , )**

r: the distance from the origin : the angle down from the z axis is called polar angle : angle around from the x axis is called the azimuthal angle

4
**The Curl of E For a point charge situated at origin:**

Line integral of the field from some point a to some other point b: In spherical polar coordinates,

5
**The integral around a closed path:**

Apply stokes theorem: True for electrostatic field.

6
**Electric Potential Basic concept:**

The absence of closed lines is the property of vector field whose curl is zero. E is such a vector whose curl is zero. Using this special kind of it’s property we can reduce a vector problem: using V, we can get E very easily. Vector whose curl is zero, is equal to the gradient of some scalar function E=0 the line integral of E around any closed loop is zero (due to Stokes' theorem).

7
**Therefore the line integral of E from point a to point b is the same for all paths.**

otherwise you could go out along path (i) and return along path (ii) and Because the line integral is independent of path, we can define a function O is some standard reference point. is called electric potential

8
**The potential difference between two points a and b:**

Using fundamental theorem for gradients: So Electric field is the gradient of a scalar potential.

9
**Electric Potential at an arbitrary point**

Electric potential at a point is given as the work done in moving the unit test charge (q0) from infinity (where potential is taken as zero) to that point. Electric potential at any point P is S.I. unit J/C defined as a volt (V) and 1 V/m = 1 N/C Note that Vp represents the potential difference dV between the point P and a point at infinity.

10
**Potential Difference in Uniform E field**

Example: Uniform field along –y axis (E parallel to dl) When the electric field E is directed downward, point B is at a lower electric potential than point A. A positive test charge that moves from point A to point B loses electric potential energy. Electric field lines always point in the direction of decreasing electric potential.

11
**Potential Diff. in Uniform E field**

Charged particle moves from A to B in uniform E field. q

12
**Potential Diff. In Uniform E field (Path independence)**

Show that the potential difference between point A and B by moving through path (1) and (2) are the same as expected for a conservative force field. By path (1),

13
path (2) = 0 since E is to dl

14
**Equipotential Surfaces (Contours)**

VC = VB ( same potential) In fact, points along this line has the same potential. We have an equipotential line. No work is done in moving a test charge between any two points on an equipotential surface. The equipotential surfaces of a uniform electric field consist of a family of planes that are all perpendicular to the field.

15
**Equipotential Surface**

Equipotential Surfaces (dashed blue lines) and electric field lines (orange lines) for (a) a uniform electric field produced by infinite sheet of charge, (b) a point charge, and (c) an electric dipole. In all cases, the equipotential surfaces are perpendicular to the electric field lines at every point.

16
**Electrostatic Potential of a Point Charge at the Origin**

Q P 16

17
**Electrostatic Potential Resulting from Multiple Point Charges**

Q2 P(R,q,f) Q1 O 17

18
**Electrostatic Potential Resulting from Continuous Charge Distributions**

line charge surface charge volume charge 18

19
Charge Dipole An electric charge dipole consists of a pair of equal and opposite point charges separated by a small distance (i.e., much smaller than the distance at which we observe the resulting field). d +Q -Q 19

20
Dipole Moment Dipole moment p is a measure of the strength of the dipole and has its direction. +Q -Q p is in the direction from the negative point charge to the positive point charge

21
**Electrostatic Potential Due to Charge Dipole**

observation point d/2 +Q -Q z q P 21

22
P q d/2 d/2 22

23
**first order approximation from geometry:**

q d/2 d/2 lines approximately parallel

24
**Taylor series approximation:**

24

25
**In terms of the dipole moment:**

25

26
**Electric Potential Energy of a System of Point Charges**

q2 q1 and we know q3

27
**The Energy of a Continuous Charge Distribution**

For a volume charge density p, Using Gauss’s Law: So: By doing integration by part: and so, If we take integral over all space:

28
**Poisson’s and Laplace’s Equation**

The fundamental equations for E: Gauss’s law then says that: This is known as Poisson’s equation. In regions where there is no charge: Poisson’s equation reduces to Laplace’s equation. This is known as Laplace’s equation.

Similar presentations

OK

Electrostatics Electrostatics is the branch of electromagnetics dealing with the effects of electric charges at rest. The fundamental law of electrostatics.

Electrostatics Electrostatics is the branch of electromagnetics dealing with the effects of electric charges at rest. The fundamental law of electrostatics.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on kotak life insurance Ppt on resistance temperature detector rtd Production in the long run ppt on tv Ppt on reaction mechanism in organic chemistry Ppt on human resources planning Ppt on natural resources and conservation major Ppt on artificial intelligence in mechanical field Ppt on famous wildlife sanctuaries in india Ppt on power electronics application Ppt on question tags youtube