Electrical Energy Potential

1. Electrical Energy Potential • Consider a positive charge q located in an electrical field of E that travels in one dimension through Δx from A to B. + - + A q B - + -

2. Cont. • The work done on the charge by the electric field is given by WAB = qExΔx J • This is valid for both +ve and -ve charges influenced by a constant electrical field. As electrical fields are vectors, direction of the field and the corresponding displacement of the charge must be indicated by a +ve or -ve sign.

3. Cont. • The work done is independent of the path taken from A to B. • Moving a charge in the opposite direction of then field increases the objects potential energy. • Releasing the charge so that it may move with the field converts its potential energy to kinetic energy.

4. Consider Work-Energy Theorem • Change in electric potential energy is a change in work. • W = qExΔx = ΔKE • The gain in kinetic energy is a loss of electric potential energy

5. Electrical Potential • The electric potential difference ΔV between two points A and B is the change in electric potential energy as a charge q moves from A to B, divided by the charge q • ΔV = VB- VA = ΔPE/q J/C or V(volt) • Electric potential energy is a scalar quantity. • ΔPE/q = ExΔx = V 1 N/C = 1 V/m

6. Cont. • The above is true for a uniform electrical field and a charge moving in one dimension. High electrical potential is near or at the +ve terminal, low potential is near or at the -ve terminal. • Released from rest a positive charge will accelerate towards regions of low electrical potential.

7. Consider a 12V car battery • The battery maintains an electrical potential of 12V across its terminals. The +ve terminal is 12V higher in potential than the -ve terminal.Every coulomb of +ve charge that leaves the +ve terminal carries 12J. The charge that moves through an external circuit ( light) towards the -ve terminal gives up 12J of electrical energy to the external device.

8. Battery cont. • When the charge reaches the -ve terminal the potential is zero, the battery takes over moving the charge from the -ve to the +ve terminal thus restoring the potential. The process then is repeated.

9. Electric Potential due to a Point Charge • The electric field of a point charge extends through space as does its electric potential. The zero point of electric potential is defined at an infinite distance from the charge. The electric potential at any distance is given by V = keq/r • The electric potential of two or more charges is the algebraic sum of the individual point charges’ potentials. (scalar quantities)

10. Potential Energy due to a Point Charge • Consider two charges being brought together, the electric potential energy is given by PE = keq1q2/r • If the charges are the same sign the PE is +ve. If they are of opposite sign s then PE is –ve. That is –ve work must be done to prevent the two charges from accelerating together.

11. Potentials and Charged Conductors • The electric potential energy between two points is related to the potential difference between those points. • AS W = ΔPE and ΔPE = q (VB-VA) then W = q (VB-VA) • No net work is required to move a charge between two points that are at the same electric potential.

12. Cont. • A conductor in electrostatic equilibrium has a net charge that resides on the surface. The electric field just outside the surface is perpendicular to the surface. All points on the charged conductor in electrostatic equilibrium are at the same potential and the electric potential is constant everywhere on the surface. The electric potential is constant everywhere inside the conductor and is the same as that on the surface.

13. The Electron Volt (eV) • An electron volt is the kinetic energy gained by an electron when it is accelerated through a potential difference of 1V. • AS 1V = 1 J/C and the charge on an electron is 1.60x10-19 C then 1 eV = 1.60x10-19 C.V or J

14. Equipotential Surfaces • This is a surface on which all points are at the same potential. No work is required to move a charge at constant speed on an equipotential surface. Equipotentials are lines drawn perpendicular to the electric field lines at varying distances r from the point source.

15. Capacitance • A capacitor is a device that temporarily stores electrical energy that can be reclaimed at a later time. It consists of two parallel metal plates separated by a distance d, each connected to one of the terminals of an electrical source. The plate connected to the +ve terminal losses electrons to the source becoming +ve charged, +Q. The plate connected to the –ve terminal gains these stripped electrons becoming –ve charged, -Q.

16. Cont. • The transfer of electrons stops when the potential difference across the plates equals the potential difference of the source. • The capacitance C of the capacitor is the ratio of the charge on a plate to the potential difference between the plates. C = Q/ΔV farad (F) = C/V • Typical capacitance ranges from 1µF to 1pF

17. Cont. • Capacitance is related to the area of the plates A and the distance between them d • C = ЄoA/d • The larger the plate and/or the smaller the distance between them the larger the capacitance. • Capacitors store a large charge that can be delivered quickly.

18. Symbols for Electrical Circuits • Electric source ( battery) + - • Capacitor • Light Bulb • Resistor • Wire of no or little resistance o

19. Capacitors in Parallel • Two capacitors connected as shown are said to be connected in parallel. The left plates have the same potential as do the right plates • The total charge stored is Qeq = Q1 + Q2 • The equivalent capacitance Qeq of a parallel combination is greater than the individual capacitance. • Ceq = C1 + C2

20. Capacitors in Series • For a series connection the magnitude of charge on the plates must be the same for all plates. Regardless of the capacitance or how many are in series, all plates connected to the +ve terminal will have a positive charge and plates connected to the –ve terminal will have a negative charge. • The equivalent capacitance is given by 1/Ceq = 1/C1 + 1/C2 The equivalent capacitance is always less than the individual capacitance.

21. Energy Stored in a Charged Capacitor • If the plates of a charged capacitor are connected by a wire, the charge will transfer from one plate to the other until both plates are uncharged. Discharge may be seen as a spark. When a capacitor is not charged both plates are neutral, plates have the same potential. Little work is required to transfer a small charge ΔQ from one plate to the other.

22. Stored Capacitance cont. • Once a charge has been transferred a small potential exists between the plates. ΔV = ΔQ/C and any additional charge to be transferred through a potential requires work. The total work needed to fill a capacitor is given by W = ½ Q ΔV Energy stored = ½ QΔV = ½ C(ΔV)2 = Q2/2C

23. Cont. • There is a limit to the capacity of a capacitor. At a point the coulomb forces between plates is so strong electrons jump across the gap. Capacitors are usually labeled with a maximum operating voltage. • Ex Blinking lights A Defibrillator

24. Dielectrics • A dielectric is an insulating material. Ex plastic rubber. Placed between the plates of a capacitor increases the capacity of the capacitor by a factor of K, the dielectric constant. Note K> 1 as C = Q/ΔV then the increase in capacitance is given by C = KQ/ΔV and C = KЄoA/d

25. Dielectrics cont. • By decreasing d one can increase the capacitance up to the limit until the maximum electric field is established and discharge will occur. • This maximum field is called the Dielectric Strength, for air this is 3x106 V/m Most material have values greater than air.