ศักย์(ศักดา)ไฟฟ้ า (Electric Potential)

• ประจุไฟฟ้ า q ที่อยในสนามไฟฟู่ ้ า จะ ไดร้ ับผลเช่นเดียวกนกั บมวลั m ที่อยู่ ในสนามความโนมถ้ ่วง • แรงไฟฟ้ า F = qE เป็นแรงอนุรักษ์ การเปลี่ยนแปลงพลงงานศั กยั ไฟฟ์ ้ า ของอนุภาคประจุ จาก a ไป b: ΔU ไม่ข้ึนกบเสั นทางการเคล้ ื่อน ประจุจาก a ไป b: ในรูป แสดงขณะที่อนุภาคประจุ q dl E มีการกระจดั ในสนามไฟฟ1 ้ า Electric Potential and Potential Difference

Electric Potential:

Electric potential difference ΔV between a and b:

2 Electric Potential and Potential

U  U b U a  qVb Va  Difference in Difference in electric potential • Electric potential V has units of / which is defined as a : 1 Volt = 1 /Coulomb • One Joule is the done in moving one Coulomb of charge through a potential difference of one Volt. • Electric field has units of Newtons/Coulomb or /meter: 1N/C = 1 J/(mC) = 1 V/m 3 Analogy between Electric and Gravitational Fields q m

EGd

q m

ΔU = qΔV = - qEd ΔU = - mgd The charge and lose potential energy and gain . 4 Kinetic Energy of a Charge Accelerated by an Electric Field • The kinetic energy acquired by an electron or a proton accelerated through a potential difference of 1000 Volts: -19 •Uba = qVba = (1.60 x 10 C)(1000 V) = 1.60 x 10-13 J = 1000 eV (electron volts) = 1 keV (kilo electron volt)  One electron-volt (1 eV) is the kinetic energy gained by an elemental charge (electron or proton) when it is accelerated through a potential difference of one Volt. 1 eV = 1.6 x 10-19 C

5 Electric Potential due to Point Charge

Electric Field:

Convention: V=0 at infinite r Q V  k (electric potential) r 6 Electric Potential due to a Point Charge

Electric potential at a Electric potential at a distance r from a positive distance r from a negative charge Q charge Q

7 Electric Potential due to a System of Point Charges

For a system of point charges Qi at distances ri from a point P:

Q1 Q r r4 4 1 P

r3 r2 Q3 Q2

An algebraic sum of scalars!

8 Example: Problem 23-23 (Giancoli)

• A +25 μC charge is placed 6.0 cm from an identical +25 μC charge. How much work would be required by an external force to move a + 0.10 μC test charge from a point midway between them to a point 1.0 cm closer to either of the charges? 6.0 cm ab +0.10C +25C+25C

Work = q(Vb-Va ) 9 ศักย์ไฟฟ้ าเนื่องจากประจุกระจายต่อเนื่อง ถาประจ้ ุกระจายอยบนวู่ ตถั ุอยางต่ ่อเนื่อง การหาศกยั รวมแบบ์ summation กจะปร็ ับเปลี่ยนเป็นการ integrate:

เมื่อ r คือระยะจากตาแหนํ ่ง P ใดๆ ถึงชิ้นส่วนเลกๆ็ ที่มีประจุ dq ที่เราพิจารณา. 10 ตวอยั ่าง การหาศักย์ไฟฟ้ าเนื่องจากประจุกระจายต่อเนื่องเป็นวงแหวน

หาศกยั ไฟฟ์ ้ า V ณ ตาแหนํ ่งที่ห่างเป็นระยะ x จากศูนยกลางวงแหวนไปตาม์ แนวแกนของวงแหวนเส้นเลกๆ็ รัศมี R ที่มีประจุ Q กระจายอยอยู่ างสม่ ่าเสมอํ

Uniformly Charged Ring 11 ตวอยั ่าง การหาศักย์ไฟฟ้ าเนื่องจากประจุกระจายต่อเนื่องบนแผ่นกลม

• Calculate the potential on the axis at a distance x from a uniformly charged disk of radius R. พิจารณาไดว้ าแผ่ นกลมประกอบข่ ้ึนจากวงแหวนเส้นเลกๆ็ รัศมี r กวาง้ dr.

12 ผวสมศิ ักย์(Equipotential Surfaces) • Equipotential surfaces are surfaces of constant electric potential (just as lines of constant elevation on a topological map are lines of constant gravitational potential). • Equipotential surfaces are always perpendicular to the direction of the electric field. (just as the “fall line” is perpendicular to the contour lines on a topological map). Charged Parallel Plates Two Equal and Opposite Charges

13 Determination of the Electric Field from the Electric Potential If the electric potential is known in space, the electric field may always be determined from it.

14 Determination of the Electric Field from the Electric Potential

The relationship between the electric field and the electric potential may be expressed in vector form:

15 Electric Potential Energy: The Electron Volt • Suppose a point charge q is moved between two points a and b in space, where the electric potentials due to other charges are Va and Vb.

• The change in potential energy is:

ΔU = Ub –Ua = q(Vb –Va) = qVba

• Unit = Electron Volt (eV): 1 eV = 1.6 x 10-19 J

• e.g. a proton accelerated through a potential difference of 200 kV acquires a kinetic energy of 200 keV (losing 200 keV of electric potential energy). 16 ตวเกั บประจ็ ุ() •A is a device that stores . เป็นอุปกรณ์ที่ใชเก้ บสะสมประจ็ ุไฟฟ้ า

• A capacitor consists of two conductors separated by an insulator.

• Capacitors have many applications: – Computer RAM memory and keyboards. – Electronic flashes for cameras. – Electric surge protectors. – Radios and electronic circuits. 17 Types of Capacitors

Parallel-Plate Capacitor Cylindrical Capacitor A cylindrical capacitor is a parallel-plate capacitor that has been rolled up with an insulating layer between the plates.

18 Capacitors and Capacitance

A capacitor in a simple electric circuit.

Charge Q stored: Q  CV

The stored charge Q is proportional to the potential difference V between the plates. The capacitance C is the constant of proportionality, measured in Farads. Farad = Coulomb / Volt 19 Parallel-Plate Capacitor • A simple parallel-plate capacitor consists of two conducting plates of area +Q -Q A separated by a distance d. • Charge +Q is placed on one plate and –Q on the +Q -Q other plate. • An electric field E is created between the plates.

20 Electric Field Inside a Parallel-Plate Capacitor

+Q -Q

21 Capacitance of Parallel-Plate Capacitor

22 Capacitors in Parallel

Q  Q1  Q2  Q3

 C1V  C2V  C3V

 (C1  C2  C3 )V

 CeqV

Capacitors in Parallel:

Ceq  C1  C2  C3 ...

23 Capacitors in Series

V  V1 V2 V3 Q Q Q    C1 C2 C3  1 1 1   Q     C1 C2 C3  Q  Ceq 1 1 1 1 For n capacitors    ... in series: Ceq C1 C2 C3 24 Circuit with Capacitors in Series and Parallel

C1 C2 15 μF 3 μF C4 20 μF ab

6 μF

C3 ?

Cab

What is the effective capacitance Cab between points a and b?

25 in Capacitors • Since capacitors store electric charge, they store electric potential energy. • Consider a capacitor with capacitance C, potential difference V and charge q. • The work dW required to transfer an elemental charge dq to the capacitor: q dW  Vdq  dq The work required to charge the c capacitor from q=0 to q=Q:

Energy Stored by a Capacitor = ½CV2 = ½QV 26 Example: Electronic Flash for a Camera

• A charges a 100 μF capacitor to 250 V.

a) How much is stored in the capacitor?

b) If the stored charge is delivered to a krypton flash bulb in 10 milliseconds, what is the power output of the flash bulb?

27 Stored of a Charged Capacitor

28 Dielectrics •A dielectric is an insulating material (e.g. paper, , glass).

• A dielectric placed between the conductors of a capacitor increases its capacitance by a factor κ, called the dielectric constant.

C= κCo (Co=capacitance without dielectric)

• For a parallel-plate capacitor:  A A C   0   d d

ε = κεo = permittivity of the material. 29 Properties of Dielectric Materials • Dielectric strength is the maximum electric field that a dielectric can withstand without becoming a conductor. • Dielectric materials – increase capacitance. – increase electric breakdown potential of capacitors. – provide mechanical support. Dielectric Dielectric Material Constant κ Strength (V/m) air 1.0006 3 x 106 paper 3.7 15 x 106 mica 7 150 x 106 6 strontium titanate 300 8 x 10 30 Practice Quiz • A charge Q is initially placed on a parallel- plate capacitor with an air gap between the , then the capacitor is electrically isolated. • A sheet of paper is then inserted between the capacitor plates. • What happens to: a) the capacitance? b) the charge on the capacitor? c) the potential difference between the plates? d) the energy stored in the capacitor?

31 The Electric • (, 1780’s) studied the effect of static on the contraction of leg muscles in frogs, and found that the same effect could be produced by inserting two dissimilar metals into the muscle. • (Italy,1800) invented the and demonstrated a flow of electric charge. Volta’s original battery consisted of A simple electric cell is the alternate layers of and silver and basis of the common 1.5 Volt a salt solution. “” battery.

32 Common Dry cell • The () reacts with the zinc dissolving part of it. • Each zinc atom enters solution as a positive , leaving two electrons behind. • The zinc electrode is left with a net negative charge. • The positively charged electrolyte pulls electrons off the electrode, leaving Common dry cell. it with a net positive charge. (AA,AAA, C or D cell) The net result is that the carbon electrode is left with a net positive charge and the zinc electrode a net negative charge, creating a potential difference between them of 1.5 V. 33 Electric Cell or Battery

• An electric cell or battery produces an electric potential difference between two conducting electrodes (terminals) by transforming into electrical energy.

++–– • Symbol: or

• The battery “dies” as one or the other of the electrodes becomes depleted.

• Some types of batteries (e.g. Ni-Cd) may be “recharged” by applying an electric potential difference, reversing the chemical process. 34 • Electric charge will flow from a battery if a conducting path (a circuit) is provided between its terminals. •TheElectric Current I Simple electric circuit. is the rate of flow of charge and must be identical at all points in a simple circuit (e.g. mass flow rate through a water hose).

dQ I  measured in  (A)

dt Second 35 Sign Convention for Electric Current • The direction of current flow is the direction of flow of positive charge (which is opposite to the direction of electron flow). • Electrons are the charge carriers in most electric circuits using metals as conductors (not always true in ).

Positive current flows from the positive terminal through the conductors and device (load) back to the negative terminal.

The circuit must be closed in order for current to flow. 36 Resistance and ’s Law • Georg Ohm (Germany, early 1820’s) determined that the current flow through a conductor is proportional to the potential difference applied to its ends. I = (constant) V = (conductance) V

Resistance = 1/(Conductance) Volt R Ohm  V=IR Ohm’s Law Ampere 37 Questions: Electric Current

1. Is the magnitude of the electric current different at different points in a simple electric circuit, such as that shown?

2. What happens to the current 3. What happens to in the circuit if the resistance the current of the device supplied by the a) is doubled? battery if two b) is halved? identical devices are connected in parallel across it? 38