1. Electrostatics Electric Potential

Recall… Gravitational Potential Energy or Elastic Potential Energy Now… Electric Potential Energy (EPE)

EPE is a type of mechanical energy, like… Kinetic Energy (KE) = ½ mv 2 Rotational Kinetic Energy (KE R ) = ½ I  2 Gravitational Potential Energy (PE grav ) = mgh Elastic Potential Energy(PE elast ) = ½ kx 2 = Total Mechanical Energy (E) is conserved if there are no non-conservative forces present (ie friction)

F = mg q F = qE W = mghW = qEx ∆U g = -W ∆U e = -W b m h g a E x Gravitational field Electric field W= - (Fcos)s

Two points are said to differ in electric potential if work is done to move a charge from one point to another point in an electric field. Work = -Δ Electric Potential Energy

Work is required to move two point charge closer together. FF r This work is converted to potential energy. This electric potential energy of two point charges:

[3] An electron starts from rest 32.5 cm from a fixed point charge with Q = μC How fast will the electron be moving when it is very far away?

Is the potential energy per unit charge. E q x a b Electrical Potential can also be described by the terms; potential difference, voltage, potential drop, potential rise, electromotive force, and EMF Units ~ J/C

Units for Electric Potential Electric potential V has units of Joules/Coulomb which is defined as a Volt: 1 Volt = 1 Joule/Coulomb One Joule is the work done in moving one Coulomb of charge through a potential difference of one Volt. Electric field has units of Newtons/Coulomb or Volts/meter: 1N/C = 1 J/(m C) = 1 V/m Difference in electric potential Difference in potential energy

Potential V is the analog of height/level/altitude/elevation h.

If a charged particle gains kinetic energy in an electric field, it loses an equivalent amount of potential energy. Point B is at a lower electric potential than is point A. Points B and C are at the same electric potential. The gain in kinetic energy depends only on the potential difference and not the path taken.

Example: Kinetic energy of an electron accelerated through a potential difference of 6,000 Volts (6 kV): 1 electron-volt (eV) is the kinetic energy gained by an elemental charge accelerated by a potential difference of 1 Volt. 1 eV = x J For a conservative force, the kinetic energy gained or lost is equal to the difference in potential energy:

[1] An electron acquires 7.45 x 10  17 J of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference and which plate is at the higher potential? AB E Plate B has a positive charge and is at a higher potential.

E q x x =1.00 cm q = 1.60 x 10  19 C E = 2000 N/C m = 9.1 x 10  31 kg [2] a) Find the speed of the charge at the lower plate. b) Find the potential through which the charge moves. m

x =1.00 cm q = 1.60 x 10  19 C E = 2000 N/C m = 9.1 x 10  31 kg d) Find the acceleration of the charge. c) Find the force on the charge as it moves. E q x m or

Make sure that we understand the difference between Potential and Electric Potential Energy: V (in Volts) = Potential a property of a certain position in an Electric Field with or without charges placed there E - EPE (in Joules) = Electric Potential Energy a property of charges placed at a certain position in an external Electric Field + - E

d E V 10 V0 V 5 V2.5 V 7.5 V 0 cm  10 cm  5 cm Let E = 100 N/C d = 10 cm Using potentials instead of fields can make solving problems much easier – potential is a scalar quantity, whereas the field is a vector. Electric Potential 17

Convention: V=0 at infinite r Electric Field: Electric Potential:

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

The electric potential due to a point charge VV +r rr VV rr Electric Potential 17

For a system of point charges Q i at distances r i from a point P: … an algebraic sum of scalars! Q1Q1 Q4Q4 Q3Q3 Q2Q2 P r1r1 r2r2 r3r3 r4r4

q r What is the Potential at this point? Notes: 1) Include the sign of q in your calculation! (+ or -) 3) The equation can also be used for a charged sphere: rTotal charge Distance from center 2) Potential Difference can also be calculated: V = V 2 – V 1 4) Electric Potential is a scalar not a vector V = V 1 + V 2 + V 3 + … (an algebraic sum, not a vector sum)

[4]What is the electric potential at a distance of 2.5 x m away from a proton? +q -q-q-q-qP d d d d [5] Find the potential V at point P due to the four charges. Web Link: Complex Electric FieldComplex Electric Field

Ans: N/C, 100 o from +ve x axis; -18,000 V; J [6] The +4 μC charge is located at 4 m on the x-axis and the -6 μC is located at +2 m on the y- axis as shown below. a) Calculate the magnitude and determine the direction of the electric fields at the origin due to the +4 μC charge and due to the -6 μC charge. b) Calculate the electric potential at the origin. c) Calculate the work done to bring a +4 μC from infinity to the origin.

Example: Approaching a Charged Sphere A proton is fired from far away at a 1.0 mm diameter glass sphere that has a charge of q=+100 nC. What is the initial speed the proton must have to just reach the surface of the glass?

Example: Moving Through a Potential Difference A proton with a speed of v i = 2.0x10 5 m/s enters a region of space where source charges have created an electric potential. What is the proton’s speed after it has moved through a potential difference of  V=100 V? What is v f if the proton is replaced by an electron?

Electrostatic Precipitator A strong electric field produces ionization of gases entering the device. Most of the tiny particulates present in the flue gas become negatively charged, and stick to the walls that are at a positive electric potential. The electrostatic precipitator is highly effective in removing tiny particulates (e.g. carbon and metals) from the flue gases of coal-burning power plants.

Cathode-Ray Tube (CRT) The electron beam is scanned in a raster pattern across the phosphors on the CRT screen. – + + –