1 ELECTROSTATICS COULUMB’S LAW ELECTRIC FIELD INTENSITY LINE, SURFACE & VOLUME CHARGES ELECTRIC FLUX DENSITY GAUSS’S LAW ELECTRIC POTENTIAL BOUNDARY CONDITIONS CAPACITANCE

2 Electrostatic Field Problem – Example: Parallel Plate Capacitor Scalar Field: Electrostatic Potential Vector Field: Electrostatic Field Strength

3 Bear in mind!!!! Electromagnetics is the study of the effect of charges at rest and charges in motion. Some special cases of electromagnetics: Electrostatics: charges at rest Magnetostatics: charges in steady motion (DC) Electromagnetic waves: waves excited by charges in time-varying motion

4 Electrostatics Electrostatics is the physics term for static charge. Electro means charge, and of course static means stationary or not moving. Charge 2 Types of Charge: Positive (+) and Negative (-)

5 Electrostatics Attraction and Repulsion Unlike a gravitational force which always attracts, electrostatic force may repel or attract depending on the type charge. Ben's Rule and Paula Abdul - Opposites attract and likes repel. (+) (-) = attract (+) (+) = repel (-) (-) = repel

6 Electrons have a negative charge and protons have a positive charge. Neutrons and most materials have a net charge of zero or neutral. When certain types of objects are rubbed together, electrons from one object may be transferred to an object with a greater affinity for the electrons. When this happens, the object that gave up the electrons is positive, whereas the object that collected the electrons is negative. Key: Only electrons move. They exist in the outer shells of the atom. Electrostatics : Microscopic View

7 ++ Asbestos Fur (rabbit) Glass Mica Wool Quartz Fur (cat) Lead Silk Human skin, Aluminum Cotton Wood Amber Copper, Brass Rubber Sulfur Celluloid India rubber -- Electric charge is inherently quantized such that the charge on any object is an integer multiple of the smallest unit of charge which is the magnitude of the electron charge e =  C. On the macroscopic level, we can assume that charge is “continuous.” The following list shows part of the tribo- electric sequence. When any two substances shown in this list are rubbed together, the top one will become positively charged while the lower one will become negatively charged. The further apart the two substances are in the list, the greater the electrification.

8 All bodies are able to take a charge of electricity and this is termed static electricity. The charge on a body is measure by means of the force between the charges. The Coulomb force law, which only applies to charged points, is stated below.. The force of attraction or repulsion between two charged points is directly proportional to the charges and inversely proportional to the square of the distance between them. In vector form, it is stated thus, Static Charges: Coulomb’s Law

9 Coulomb’s Law Where; F = Force between points (N) Q 1, Q 2 = Charges on point 1 and point 2 (Coulomb) R = radial separation on points/distance (m) = Permittivity of the free space (vacuum) with a value given by: = the unit vector in the direction from Q 1 to Q 2

10 Charge Q 1 exerts a vector force F 12 in Newton's (N) on charge Q 2, Coulomb’s Law Note: a negative force results if the points have opposite charges and a positive force results if the points have the same polarity

11 The proportional constant, k is: Coulomb’s Law The above equation can be simplified as follows is constant= 8.99x10 9

12 If the space between the charges is another material or air, the law may be written where relative permittivity of material. Coulomb’s Law

13 Example 1 Find the force on charge Q1, 20  C, due to charge Q2, -300  C, where Q1 is at (0,1,2)m and Q2 at (2,0,0)m x z y Q1 Q2 F1 R 21 (0,1,2) (2,0,0) Solution 1

14 Solution 1 (cont’d) Because 1C is a rather large unit, charges are often given in microcoulombs (  C), nanocoulombs (nC) and picocoulombs (pC). Referring to figure, R 21 =-2a x +a y +2a z  R=3 a 21 =1/3(-2a x +a y +2a z )  The force magnitude is 6N and the direction is such that Q 1 is attracted to Q 2 (unlike charges attract)

15 Electric Field Intensity If Q 1 is fixed to be at origin, a second charge Q 2 will have force acting on Q 1 and can be calculated using Coulomb’s Law. We also could calculate the force vector that would act on Q 2 at every point in space to generate a field of such predicted force values.

16 It becomes convenient to define electric field intensity E 1 or force per unit charge as: This field from charge Q 1 fixed at origin results from the force vector F 12 for any arbitrarily chosen value of Q 2 Electric Field Intensity (Cont’d)

17 Coulomb’s law can be rewritten as to find the electric field intensity at any point in space resulting from a fixed charge Q. Electric Field Intensity (Cont’d)

18 Example 2 Thus in the direction Solution to Example 2 Find E at (0,3,4) m in cartesian coordinates due to a point charge Q =0.5  C at the origin.

19 Let a point charge Q 1 = 25nC be located at P 1 (4,-2,7). If ε = ε 0, find electric field intensity at P 2 (1,2,3). Example 3 By using the electric field intensity, This field will be: Solution to Example 3

20 Where, and Solution to Example 3 (Cont’d)

21 Electric Field Intensity (Cont’d) If there are N charges, Q 1,Q 2...Q N located respectively at point with position vectors r 1,r 2...r N the electric field intensity at point r is:

22 Field Lines The behavior of the fields can be visualized using field lines: Field vectors plotted within a regular grid in 2D space surrounding a point charge.

23 Some of these field vectors can easily be joined by field lines that emanate from the positive point charge. The direction of the arrow indicates the direction of electric fields The magnitude is given by density of the lines Field Lines (Cont’d)

24 The field lines terminated at a negative point charge The field lines for a pair of opposite charges Field Lines (Cont’d)