Electric Potential, Energy and Capacitance

1. Electric Potential, Energy and Capacitance

2. Energy • Electricity is how we transport and expend a large part if not the bulk of our energy resources. • So far we’ve only talked about how to quantify electrical forces with Coulomb’s law and electric field.

3. Voltage (potential) • You likely think of voltage first when electricity comes to mind; • 110 volt ac residential outlets • 12 volt car battery • 3.7 volt cell phone battery • …

4. Voltage Defintion • Voltage is defined as the potential energy per charge. This is where the term “potential” comes from.

5. Electrical Potential Energy • Similar to the way gravitational potential energy was expressed, we can show that electrical potential energy is given by:

6. Potential due to a point charge • V is the electrical potential (voltage) at a distance r from a point charge

7. Voltage is a scalar • Means you can just add it, no trig! A r1=0.8 m r2=1.2 m q2 q1 -4.5 mC 3.5 mC

8. Let’s work it out. A r1=0.8 m r2=1.2 m q2 q1 What is the potential at point A? -4.5 mC 3.5 mC

9. Potential Difference • What is the potential difference between points A and B. B 2.0 m 1.0 m A r1=0.8 m r2=1.2 m q2 q1 -4.5 mC 3.5 mC

10. Work it out. • Calulate the potential at B, • Subtract(difference) the potential at A

11. Why should we care? • It’s about energy, we want to be “green” in all we do and save resources for the future. • So let’s see how this helps with energy.

12. How much work is done… • …Moving an electron from A to B? • Work done by the electric fields is the negative of the PE change. • Work done by an external force is the PE change. • Let’s just deal with external forces for our example. Voltage and energy are scalars, that means they are path independent.

13. Work • So for our electron, W=-1.6x10-19( ) = J Note, it is common to express small amounts of energy in electron-volts, eV. Basically just drop the elementary charge, so W=()eV

14. Capacitors • Capacitors are electrical devices that store energy, usually temporarily. • Batteries store chemical energy that can be transformed into electrical energy. • Capacitors store energy electrically, by storing electrical charge.

15. Construction • Two conducting plates, separated by a small distance. • Electrons are taken from one plate and put on the other. • They will end up being at different voltages, so energy is released when the charge travels through a device such as a motor, light, speaker etc. to the other plate of the capacitor

16. Picture

17. Charge stored C is capacitance and can be determined by: A is the area of the plates d is the distance between them e0 is a constant K is the dielectric constant, a property of the material between the plates, for air = 1.0 Units of capacitance are Farads=coulombs per volt Typically small values, micro, pico

18. Energy stored • As charge increases, so does the voltage and the work required to move an electron from one plate to the other… • …so it’s like the energy in a spring.

19. Note! • The units for electric field are Newtons per Coulomb, which is dimensionally equivalent to • Volts per meter… • So the Electric field between two plates is easily calculated. • Divide voltage by plate separation. • Since the field between two plates is uniform, • The work to move a charge from one plate to the other is; • W=qEd

20. Example • What is the capacitance of two plates .055 m2, separated by 0.10mm of air? • How much charge is stored when the voltage between the plates is 100 volts? • How much energy is stored at 100 volts?

21. Review

22. Questions?