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Chapter 17

Chapter 17. Electric Charge and Electric Field. Two kinds of charges: positive and negative. Two charges of the same kind REPEL each other Two charges of different kinds ATTRACT each other. Coulomb’s Law.

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Chapter 17

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  1. Chapter 17 Electric Charge and Electric Field

  2. Two kinds of charges: positive and negative • Two charges of the same kind REPEL each other • Two charges of different kinds ATTRACT each other

  3. Coulomb’s Law • The magnitude F of the force that each of two point charges q1and q2 exerts on each other when they are separated by a distance r is directly proportional to the product of the two charges and inversely proportional to the distance squared F = k |q1q2|/r2

  4. Additive forces r12 r23 q1 q2 q3 r13

  5. ELECTRIC FIELD

  6. GAUSS’s LAW The total flux ΦE coming out of any closed surface is proportional to the total electric charge Qencl inside the volume surrounded by this surface. ΦE = Qencl / ɛo Ɛo = 8.854x10-12C2/(N.m2)

  7. Chapter 18 Electric Potential and Capacitance

  8. ELECTRIC POTENTIAL ENERGY Electric potential energy is between two charges (q and q’ ) separated by a distance r and is defined as: PE = kqq’/r Electric potential energy is a scalar and has units of Joule (J). When there are more than 2 charges, the total potential energy is the sum of the energy associated with each pair of charges

  9. In the gravitational case, the change in the potential energy associated with an object with mass m when moved from the surface to a height h is mgh Similarly, the electric potential energy associated with a charge q in a field E is: qEd When the charge is moved a distance d along or opposite direction of the field

  10. ELECTRIC POTENTIAL or VOLTAGE • A charge Q creates an electric field around it. Similarly, this charge will create an electric potential V around it, commonly called voltage It is a scalar and is defined as: V = kQ/r The unit for electric potential is the Volt (V). Consequently, when a charge q is placed at a distance r from Q, the electric potential energy between the two charges would be: U = qV

  11. ELECTRIC POTENTIAL and ELECTRIC FIELD • For parallel plates separated by a distance d and a potential difference between them V the field between the plates is then: E= V/d Or V=Ed

  12. DEFINITION • The CAPACITANCE C of a capacitor is the ratio of the magnitude of the charge Q on either conductor (plate) to the magnitude of the potential Vabbetween the conductors (plates): C =Q/Vab The SI unit of capacitance is FARAD (1farad = 1C/1V)

  13. CAPACITANCE FOR PARALLEL PLATES • If the capacitor is made of parallel plates with surface area A and a separationd between the plates, the capacitance is: C = ɛ0A/d

  14. Capacitors are often joined

  15. Capacitors are often joined II – Figures 18.22

  16. Electric Field Energy in a Capacitor • One of the applications of the capacitor is to store energy (analogous to the potential energy stored in a spring) Ucapacitor = (1/2) CV2

  17. Chapter 19 Current, Resistance, and Directed-Current Circuits

  18. Current defined Unit: 1coulomb/second = 1 ampere = 1A

  19. Resistance and Ohm’s Law • When the potential difference Vbetween the two ends of a conductor is proportional to the current Ipassing through the conductor, the ratio (V)/(I) is called the resistance of the conductor : R = V/I The SI unit for resistance is the ohm and it is represented by the Greek letter Ω 1Ω = 1V/A

  20. Resistivity • The resistance is the property of a given conductor and it depends on its length L and cross- section area A R = ρ L/A L ρ characterizes the conduction properties of the material

  21. Power in Electric Circuit The power P is defined as P = VabI The unit for power is the watt 1W = 1J/s

  22. Power for a pure resistor: For a pure (single) resistor, we have: P=VabI Since V= RI P = RI2 or P = V2ab/R

  23. Connections in series Req = R1 + R2 + R3 SAME CURRENT DIFFERENT POTENTIAL

  24. Connections in parallel 1/Req = 1/R1 + 1/R2 + 1/R3 SAME POTENTIAL DIFFERENT CURRENT

  25. Chapter 20

  26. Charges moving with respect to a field

  27. Charges moving with respect to a field

  28. Charges moving with respect to a field

  29. UNIT FOR MAGNETIC FIELD • The magnetic field B has unit, in SI : TESLA 1 tesla = 1T=1N/(A.m)

  30. The effect of the sign of a moving charge

  31. Magnetism and circular motion F = |q|vB If the motion is Circular F = mv2/R R = mv/ |q|B ω = v/R = |q|B/m

  32. Force on a conductor with current F = ILB

  33. The motor and torque  = (IaB)bsinΦ

  34. Magnetic field of long straight conductor

  35. Magnetic field of a long, straight wire: B = μ0I/(2πr) r is the distance from the wire μ0 is called the permeability of vacuum μ0 = 4π x 10-7 T.m/A

  36. Fields in two conductors side-by-side

  37. 2 wires with currents flowing in the same direction attract each other 2 wires with currents flowing in opposite directions repel each other F =μ0 L(I1 I2)/(2πr) Force per unit length F/L =μ0 (I1 I2)/(2πr)

  38. Currents in a loop Magnetic field at the center of a circular loop B = μoI /(2R) For N loops: B = μo NI /(2R)

  39. SOLENOID Magnetic field of a Solenoid: B = μonI n = number of turns per unit length n = N/L

  40. Chapter 21 Electromagnetic Induction

  41. Does the field induce a current or not?

  42. Magnetic flux at various orientations

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