Previous Lecture Introduced Electrostatic Potential Energy Uel Electric

Previous Lecture Introduced Electrostatic Potential Energy (Uel) Electric Potential (V) Learned how to compute V for • point charge • charged sphere

Potential Energy Introduced the concept of electric field E to deal with forces Introduced electric potential V to deal with work and energy Electric potential: electric potential energy per unit charge Potential energy is associated with pairs of interacting objects A single particle has no electric potential energy

Potential Difference with Varying Field In general, integration path may be complex

Sign of the Potential Difference The potential difference V can be positive or negative. The sign determines whether a particular charged particle will gain or lose energy in moving from one place to another. If q V < 0 – then potential energy decreases and K increases If q V > 0 – then potential energy increases and K decreases If there are no external forces acting on the system:

Example x An electron traveling to the right enters capacitor through a small hole at A. Electric field strength is 2 x 103 N/C. What is the change in the electron’s potential energy in traveling from A to B? What is its change in kinetic energy? (AB)= 4 mm = (1. 6 x 10 -19 C)(2 x 103 N/C)(0. 004 m) =1. 3 x 10 -18 J K = - Uelectric = -1. 3 x 10 -18 J

Example 300

Question 1 A proton is free to move from right to left in the diagram shown. There are no other forces acting on the proton. As the proton moves from right to left, its potential energy: A) B) C) D) Is constant during the motion Decreases Increases Not enough information V 1 < V 2

Sign of the Potential Difference If freed, a positive charge will move to the area with a lower potential: Vf – Vi < 0 (no external forces) V 1 < V 2 Moving in the direction of E means that potential is decreasing

Question 2 A system consists of a proton inside of a capacitor. The proton moves from left to right as shown at a constant speed due to the action of an external agent. Which of the following statements are true? A) The proton’s potential energy is unchanged and the external agent does no work on the system. B) The proton’s potential energy decreases and the external agent does work W > 0 on the system. C) The proton’s potential energy decreases and the external agent does work W < 0 on the system. D) The proton’s potential energy increases and the external agent does work W < 0 on the system. E) The proton’s potential energy increases and the external agent does work W > 0 on the system. V 1 < V 2

Shifting the Zero Potential In most cases we are interested in V, not the absolute values of V

Potential Difference in a Nonuniform Field C x From A to C: V 1 = -E 1 x(x. C-x. A); From C to B: V 2 = -E 2 x(x. B-x. C); So, A to B: V = V 1+ V 2 = -E 1 x(x. C-x. A) - E 2 x(x. B-x. C)

Potential Difference: Path Independence f i Path independence principle: V between two points does not depend on integration path

Example: Two Different Paths in Capacitor Need to find VAC =VC - VA 1. Straight path A C

Example: Two Different Paths in Capacitor Need to find VAC =VC -VA 1. Straight path A C 2. Path A B C

Example: Different Paths near Point Charge 1. Along straight radial path: rf ri +q

Example: Different Paths near Point Charge 2. Special case i. A: AB: BC: + Cf:

Example: Different Paths near Point Charge 3. Arbitrary path +

Round Trip Potential Difference + Potential difference due to a stationary point charge is independent of the path Potential difference along a closed loop is zero A vector field is a conservative field if we can find a potential (scalar function) so that the vector field is the gradient of the potential.

Predicting Possible Field Configuration Is the following “curly” pattern of electric field possible? dl dl is always parallel to dl This “curly” pattern of electric field is impossible to produce by arranging any number of stationary point charges!

Potential in Metal In static equilibrium A Capacitor with large plates and a small gap of 3 mm has a potential difference of 6 Volts -Q +Q from one plate to the other. Find E E -3 V +3 V d =3 mm V = 6 Volt Charges are on surface

Potential in Metal In static equilibrium -Q 1 1 mm +Q 1 Insert a 1 mm thick metal slab into the center of the capacitor. Metal slab polarizes and has charges +Q 2 and -Q 2 on its surfaces. What are the charges Q 1 and Q 2? E inside metal is zero Q 2=Q 1 Now we have 2 capacitors instead of one d =3 mm V = 4 V Charges +Q 2 and –Q 2 V inside metal slab is zero! There is no “conservation of potential”!

Physics of lightning Free path of e- in air at 1 atm, room T is about 1 micron (1*10 -6 m) Ionization potential of O 2 is 12. 5 e. V, N 2 15 e. V (1 e. V=1. 6*10 -19 J is a kinetic energy which e- gains by going through V=1 Volt) Approximate that about 10 V is needed to ionize air. So, what will be E= V/ x = 10/10 -6 = 107 V/m (close to E critical = 3*106 N/C we used in Lecture 7) http: //www. alexandrosmaragos. com/2012/07/lightning-captured-at-7207 -f

Electron-Volt (e. V) – Unit of Energy What is the change in electric potential energy associated with moving an electron from 1Å to 2Å from a proton? If an electron moves through a potential difference of 1 V there is a change in electric potential energy of 1 e. V = e. (1 V) = (1. 6. 10 -19 C)(1 V) = 1. 6 10 -19 J

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