PHYS219 Fall semester 2014 Lecture 05: Electrostatic Potential and Capacitors Dimitrios Giannios Purdue University

From electric potential energy to electric potential + rq test PE E 2q test 2PE E Q potential energy electric potential (remember how from F E  E = F E /q)

NEW Concept: The Electric Potential V The electric potential V at a location in space is the measure of how much electric potential energy will be generated by placing a charge +q test at that location Units of Electrostatic Potential: Electrostatic Potential = Electrostatic Potential Energy Charge = Joules = Volt Coulomb 2 ( )

q The Electric Potential V for a Point Charge q

For a system of point charges, what is the electrostatic potential V at point A? +q test Note: i)Here, q 1, q 2, etc. are SIGNED quantities ii) The potential V does NOT depend on q test

5 r 5 = 4.0 μm P X q 1 =10.0 pC r 2 = 4.7 μm q 3 =-8.0 pC q 2 =25.0 pC q 4 =5.0 pC q 5 =-15.0 pC r 1 = 8.0 μm r 3 = 3.5 μm r 4 = 5.0 μm Example: What is the electrostatic potential at point P? Note: 1 pC=1 x C; 1 μm = 1 x10 -6 m

Electrostatic Equipotentials Can be measured with an altimeter! Gravitational Equipotentials: contour lines on a topographic map Visualizing the Electric Potential Equipotential Surfaces Can be measured with an electrostatic voltmeter!

Example: The electric potential difference between a storm cloud and earth is 100 million volts. If 2 C of charge is dumped from the cloud into earth, what is the change in potential energy of the charge? 2C ΔV = 100 x 10 6 V The potentially damaging potential

Example: A point charge of +25 μC is moved from Point A to Point B. How much work is required? x B 10 V 20 V 50 V 30 V 40 V 60 V Path I Path II Path III AxAx You can show that q test

The discussion today may seem abstract, but it lays the groundwork for analyzing electrical circuits. A q test Δ(PE E ) = q test Δ V B From concepts to real life

If you understand this material, you should be able to distinguish between two closely related concepts The electrostatic potential can be high, but the electrostatic potential energy can be quite low IF a small amount of charge is involved. The energy transferred when charging or discharging is related to changes in the electrostatic potential energy. Electrostatic Potential Energy (J) vs. Electrostatic Potential (V) Note

How Can You Store a Lot of Charge? Capacitors store charge and so store energy Parallel Plate Capacitor Capacitors

Charging up a Capacitor EXPERIMENT Voltage across Plates Charge Transferred δVδV δQδQ How much work do I have to do to move the charge δ Q? What happens to my effort? V Q work done by electric forces: W = -Δ(PE E ) = -V(δQ)

NOTE: Each plate has the same amount of charge: positive on one plate and negative on the other. The total charge is zero. Units of capacitance C is Coulomb/Volt = [Farad] or [F] Capacitance is a very general concept. It applies to any two objects, even if they are not parallel plates. Capacitance C of capacitor: ability to store charge

Example: Understanding the definition of capacitance

The standard, simple model for a parallel plate capacitor E inside is uniform to a good approximation. E outside is zero to a good approximation Note 1: ε o =8.85 × C 2 /(Nm 2 ) Note 2: C depends on geometry Note 3: A is area of one plate -12 parallel plate capacitor filled with air

=1 cm =1 mm What is the Capacitance? air-filled