Chapter 23Coulomb’s Law, ReviewElectric Field: the definition of this conceptElectric Field Lines, a way to illustrate the fieldMore cases on how to draw electric field linesAn even more general case: Electric Field Lines when the source charge is not seenHow to calculate the electric field generated by a point source charge qHow to calculate electric field generated by many charges? Superposition with electric field from each charge.Slide 9Examples on how to calculate electric field from a continuous charge distributionSlide 11Slide 12Charge Particles Experience Force in an Electric FieldTwo examplesPreview sections and homework 1/22, due 2/3Chapter 231. A review on Coulomb’s Law2. Define Electric Field3. Define Electric Field Line4. Examples on How to Calculate for the Electric Field5. Charge Particles Experience Force in an Electric Field6. Quiz 1/22Coulomb’s Law, ReviewThe formula:The units (SI): Charge: coulomb (C)Distance: meterForce: NewtonThe constants: Ke, the Coulomb constant: ke = 8.9876 x 109 N.m2/C2 = 1/(4π ε o)εo the permittivity of free space: ε o = 8.8542 x 10-12 C2 / N.m2=1 22e eq qF kr1 212 122ˆeq qkr=F rrorElectric Field: the definition of this conceptThe electric force acts through space, i.e., the effect is produced even with no physical contact between objects. One way to offer an explanation (we met this situation before, what is that?), as Faraday initiated, is the concept of a field in terms of electric fields. An electric field is postulated to exist in the region of space around a charge (of called the source charge). The strength and direction of that electric field at a point in space is then measured by the force of the electric field exerts on another charge (often called the test charge) at that point. Mathematically:The electric field, , is a vector. The test charge, qo, is usually a very small charge compared with the source charge, so that its existence does not distort the electrical field generated by the source charge. Unit: Newton/Coulomb or N/C. Eroq�FErrElectric Field Lines, a way to illustrate the fieldElectric field is introduced to explain the fact the electric forces act through space. We use a set of specially defined lines to illustrate the field. The lines do not exit in space, but they should do in your mind, and you must be able to “see” them with your mind’s eyes.Now let’s define these electric field lines:They start from positive charge, end at negative charge. Their density in space (number of lines in unit volume) indicates the field strength.The tangent of an electric field line at a given point points to the direction of the field at that point. Hence no lines can cross. Field lines of one point positive source charge in spaceField lines of one point negative source charge in spaceMore cases on how to draw electric field lines Electric dipole: the charges are equal and opposite. The charges are equal and positive.Can you draw for the case charges are equal but negative?A slightly more general case: the charges are not equal, not the same polarity.An even more general case: Electric Field Lines when the source charge is not seenElectric field may not come from static source charges. So there is need to just draw electric field lines to represent the electric field. In the case in the right side figure:The density of lines through surface A is greater than through surface B. So the magnitude of the electric field is greater on surface A than BThe electric field strength (number of lines) times the surface area (A or B) is called the electric flux.How to calculate the electric field generated by a point source charge qFrom the definition:Place the test charge q0. The force on q0 is given by Coulomb’s law: Then, the electric field will be The electric field only depends on the source charge, not the test charge.2ˆoe eqqkr=F rr2ˆeeoqkq r= =FE rrroq�FErrHow to calculate electric field generated by many charges? Superposition with electric field from each charge.= =� �r r2ˆii e ii iiqkrE E r=r2ˆii e iiqkrE rWhen the charges are still point charges:fromtoExample (23.5, page 653):If you do not feel comfortable about the math here, raise your hand.How to calculate electric field generated by many charges? Superposition with electric field from each charge.=r2ˆedqd krE rWhen the charges are distributed over volume V:fromto=�r2ˆeVdqkrE rAgain if you do not feel comfortable about the math here, raise your hand.Examples on how to calculate electric field from a continuous charge distributionExample 23.6 (page 656)Examples on how to calculate electric field from a continuous charge distributionExample 23.7 (page 657)Examples on how to calculate electric field from a continuous charge distributionExample 23.8 (page 658)Charge Particles Experience Force in an Electric FieldFrom the definition of electric field:We know that charge particles experience force in an electric field:This formula, although a simple transformation from the definition, is a lot more useful.eq=F Er r�rrqFETwo examplesExample 23.9 (page 662)Example 23.10 (page 663)Preview sections and homework 1/22, due 2/3Preview sections:Section 24.1Section 24.2Homework:Problem 12, page 667.Problem 36, page
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