Chapter 30 Potential & Field Potential & Field Chapter 30. Reading Quizzes Chapter 30. Reading Quizzes 2 1 What quantity is represented by What quantity is represented by the symbol ? the symbol ? A. Electronic potential A. Electronic potential B. Excitation potential B. Excitation potential C. EMF C. EMF D. Electric stopping power D. Electric stopping power E. Exosphericity E. Exosphericity 3 4
What is the SI unit of capacitance? What is the SI unit of capacitance? A. Capaciton A. Capaciton A. Capaciton A. Capaciton B. Faraday B. Faraday C. Hertz C. Hertz D. Henry D. Henry E. Exciton E. Exciton 5 6 The electric field The electric field A. is always perpendicular to an A. is always perpendicular to an equipotential surface. equipotential surface. B. is always tangent to an B. is always tangent to an equipotential surface. equipotential surface. C. always bisects an equipotential C. always bisects an equipotential surface. surface. D. makes an angle to an equipotential D. makes an angle to an equipotential surface that depends on the amount surface that depends on the amount of charge. of charge. 7 8
This chapter investigated This chapter investigated A. parallel capacitors A. parallel capacitors A. parallel capacitors A. parallel capacitors B. perpendicular capacitors B. perpendicular capacitors C. series capacitors. C. series capacitors. D. Both a and b. D. Both a and b. E. Both a and c. E. Both a and c. 9 10 Finding Electric Field from Connecting Potential and Field Potential and Vice Versa 11 12
EXAMPLE 30.4 Finding E from Finding the Electric Field from the slope of V the Potential QUESTION: In terms of the potential, the component of the electric field in the s -direction is Now we have reversed Equation 30.3 and have a way to find the electric field from the potential. EXAMPLE 30.4 Finding E from EXAMPLE 30.4 Finding E from the slope of V the slope of V
EXAMPLE 30.4 Finding E from EXAMPLE 30.4 Finding E from the slope of V the slope of V EXAMPLE 30.4 Finding E from the slope of V 20
Kirchoff’s Laws Batteries and emf 1. Junction Law. Net current at a junction is zero The potential difference between the terminals of an ideal (Conservation of Charge) battery is � � = I I in out In other words, a battery constructed to have an emf of 1.5V creates a 1.5 V potential difference between its 1. Loop Law. The sum of all potential differences around a positive and negative terminals. closed path is zero (Conservation of Energy) The total potential difference of batteries in series is simply the sum of their individual terminal voltages: 21 22 Electrical Circuit Potential and Current � A circuit diagram is a simplified representation of an actual circuit � Circuit symbols are used to represent the various elements � Lines are used to represent wires � The battery’s positive terminal is where R = � L/A where R = � L/A indicated by the longer line 23 24
Electrical Circuit Electrical Circuit ∆ V − + The battery is characterized by the voltage – the potential difference between the contacts of the battery In equilibrium this potential difference is equal to − + the potential difference between the plates of the capacitor. capacitor. V ∆ − + − + Then the charge of the capacitor is Q = C V ∆ If we disconnect the capacitor from the battery the V ∆ capacitor will still have the charge Q and potential − − + − + + V difference ∆ Conducting wires. In equilibrium all the points of the 25 26 wires have the same potential Electrical Circuit Capacitors in Parallel ∆ V V ∆ − + − + Q = C V ∆ C 2 ∆ V − + ∆ V − + − + C 1 If we connect the wires the charge will disappear If we connect the wires the charge will disappear ∆ V All the points have and there will be no potential difference All the points have the same potential the same potential − + V 0 ∆ = V ∆ V ∆ The capacitors 1 and 2 have the same potential difference Q = C ∆ V Then the charge of capacitor 1 is 1 1 Q C V = ∆ The charge of capacitor 2 is 27 28 2 2
Capacitors in Parallel Capacitors in Parallel ∆ V − + � The capacitors can be replaced with Q C V = ∆ The total charge is 2 2 C C one capacitor with a capacitance of 2 eq Q Q Q = + 1 2 � The equivalent capacitor must have ∆ V Q C V C V ( C C ) V = ∆ + ∆ = + ∆ exactly the same external effect on the − + 1 2 1 2 Q C V = ∆ 1 1 circuit as the original capacitors C 1 This relation is equivalent to the following one Q = C ∆ V eq C Q C V = ∆ − + eq eq − + ∆ V C C C = + eq 1 2 − + 29 30 Capacitors Capacitors in Series V V ∆ ∆ 1 2 − + − + C C C 2 1 1 − + The equivalence means that − + Q C V = ∆ eq V ∆ V V V ∆ = ∆ + ∆ 1 2 − + V ∆ 31 32
Capacitors in Series Capacitors in Series � An equivalent capacitor can be found Q = C ∆ V Q = C ∆ V 1 1 2 2 that performs the same function as the The total charge is equal to 0 Q = Q = Q series combination 1 2 � The potential differences add up to the Q Q V V ∆ ∆ battery voltage ∆ V = ∆ V + ∆ V = + 1 2 1 2 − + C C − + 1 2 C C C 2 Q 1 V ∆ = C eq 1 1 1 = + − + C C C eq 1 2 V ∆ C C 1 2 C = eq C C + 1 2 33 34 Quiz: Find the equivalent capacitance for the circuit. Example in parallel in parallel C = C + C = + 1 3 = 4 C = C + C = + 1 3 = 4 eq 1 2 eq 1 2 C C = = C C + + C C = = 6 6 C C = = C C + + C C = = 6 6 eq 1 2 eq 1 2 C C C 8 C C C 8 = + = = + = eq 1 2 eq 1 2 in series in series C C 8 8 ⋅ C C 8 8 ⋅ C 1 2 4 C 1 2 4 = = = in parallel = = = in parallel eq eq C + C 8 + 8 C + C 8 + 8 1 2 1 2 in parallel in parallel 35 36
Quiz: what are the charges stored? Q C V = ∆ 37 38 Energy Stored in a Capacitor � Assume the capacitor is being charged and, at some point, has a charge q on it � The work needed to transfer a small charge from one plate to the other is ∆ q equal to the change of potential energy A q q dW Vdq dq = ∆ = C − q B � If the final charge of the capacitor is Q, then the total work required is Q q 2 Q � W dq = = C 2 C 0 39 40
Energy Stored in a Capacitor Energy Stored in a Capacitor: Application 2 2 Q q Q Q 1 1 � 2 W dq U Q V C ( V ) = = = = ∆ = ∆ C 2 C 2 C 2 2 0 � The work done in charging the capacitor is One of the main application of capacitor: equal to the electric potential energy U of a Q C V = ∆ � capacitors act as energy reservoirs that can be capacitor slowly charged and then discharged quickly to Q provide large amounts of energy in a short pulse 2 Q 1 1 2 U Q V C ( V ) = = ∆ = ∆ 2 C 2 2 Q − Q C V = ∆ Q This applies to a capacitor of any geometry − Q 41 42 The Energy in the Electric Field The energy density of an electric field, such as the one inside a capacitor, is The energy density has units J/m 3 . 43 44
Dielectrics • The dielectric constant, like density or specific heat, is a property of a material. • Easily polarized materials have larger dielectric constants than materials not easily polarized. • Vacuum has � = 1 exactly. • Vacuum has � = 1 exactly. • Filling a capacitor with a dielectric increases the capacitance by a factor equal to the dielectric constant. 45 46 General Principles Chapter 30. Summary Slides Chapter 30. Summary Slides
General Principles General Principles Important Concepts Important Concepts
Applications Applications What total potential difference is created by these three batteries? Chapter 30. Questions Chapter 30. Questions A. 1.0 V B. 2.0 V C. 5.0 V D. 6.0 V E. 7.0 V
What total potential difference is Which potential-energy created by these three batteries? graph describes this electric field? A. 1.0 V B. 2.0 V C. 5.0 V D. 6.0 V E. 7.0 V Which potential-energy graph describes this Which set of equipotential surfaces electric field? matches this electric field?
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