Electric Potential Energy & Electric Potential
Consider the following scenario. F E F E pt.a If we release the ve charge from pt.a The ELECTRIC FIELD produced by the ve charge pulls the ve charge to the left because opposites attract!
F E What if we want to move the charge to pt. B? F E pt.a d pt.b WORK! ENERGY! Where did the energy go?? There already is a force being exerted to the left by the electric field created by the ve charge In order to move a charge from pt.a pt.b, we need to exert a FORCE OVER A DISTANCE to the right
Let s refer back to gravity. Gravitational Potential Energy Pt. B is at a Higher Potential than Pt. A in the Gravitational Field pt.b pt.a F g ENERGY! WORK! In order to move a mass from pt.a pt.b we need to exert a FORCE OVER A DISTANCE The same concept applies electrically!!! Where did the energy go??
Defining Electric Potential Energy F E F E pt.a pt.b Higher Electrical Potential Energy There s a difference between pt.a & pt.b in the field Pt. B represents higher ELECTRIC POTENTIAL ENERGY in the electric field than Pt. A Remember energy is conserved!!!
Comparing Laws Gravitational Forces Electrical Forces F G = GMm F E = kq 1 q 2 r 2 r 2 F g = mg F E = qe E g = GMm r E E = kq 1 q 2 r Electric potential energy is stored by 2 separated charges just as gravitational potential energy is stored by 2 separated masses but E E can be for charges that either attract or repel
Electric Potential Energy If work is done by the electric force on a charge: W = F E d W = qε d then E E = W To calculate energy stored in a system of 2 charges a distance r apart: E E = kq 1q 2 r ***Include signs of charges when calculating E E NOTE: E E is a scalar quantity measured in J; W and E E are independent of the path taken by a charge as F E is a conservative force like F g.
Electric Potential Energy When 2 charges are ALIKE, E E is ve for repulsion. As work is done on the system to bring the opposing charges together, r and E E is stored. As r, E E, E k.. When 2 charges are OPPOSITE, EE is ve for attraction. Work is not done on the system to bring the opposing charges together; they will move towards each other naturally as work is done by the charges, r and E E. Greater E E means E k. If work was done to separate the charges, r and E E would becoming less negative. *Attraction is similar to E g graph. As r E E 0
Summary of E E When work is done against the natural tendency of the charges E E as W = E When calculating E E include the sign of the charge to indicate whether work (W) is done on the system ve (energy is added; E E ) or ve (energy is lost to kinetic energy and other forms as E E ) If W is ve, then charges are alike and want to repel; if W is ve charges are opposite and attract each other
Summary of E E If the charges are LIKE (, or,) E E is POSITIVE (ve work is done on the system against the electric field by moving charges closer together) If the charges are OPPOSITE (,) E E is NEGATIVE (ve work is done by the electric field to separate charges as E E other forms of energy in the system) For charge separation as r E E ZERO
Reality Check: What is this useful for?!?! Inkjet printers TVs and computer monitors Understanding the human body (giant electric circuit) Xrays, EKGs Radiation therapy Particle accelerators
Example 1 a)calculate the electric potential energy stored between two protons in a helium nucleus if the charge of the protons is q=1.602x10 19 C and they are 3.0x10 16 m apart. b)what is the electric force between the protons?
Gravitational Potential Energy F g If we release a mass from a point of high E g, as it falls it loses E g transferred into E K or useful work Same applies for Electric Potential Energy!
Electric Potential Energy Charges moving from higher potential energy lower potential energy = USEFUL ENERGY
Electric Potential F E F E pt.a pt.b Difference in Potential Energy per charge = ELECTRIC POTENTIAL No matter how much charge we move, each Coulomb of charge (q) will undergo THE SAME change in Electrical Potential Energy E E = ELECTRICAL POTENTIAL
Electric Potential Electric Potential Energy per unit positive test charge = ELECTRIC POTENTIAL V = E E q V = Electric Potential (J/C or Volts,V) E E = Electrical Potential Energy (J) q = magnitude of the test charge (C) ***Include signs when calculating V Electric potential is also measured in electron volts where 1eV = 1.602x10 19 C x 1V = 1.602x10 19 J 1V is the electric potential at a given point in an electric field if 1J of work is required to move 1C of charge from infinity to that point or from one point to another V = 0 at infinity as E E = 0 at infinity (reference pt.)
Electric Potential Difference Electric Potential Difference = the amount of work required per unit test charge to move a ve charge from one pt. to another pt. in the presence of an electric field If the charge is moving in the direction of the field, the electric potential decreases and is converted into kinetic energy and thermal energy If the charge is moving in the direction against the field, the electric potential increases as work is done against the force of the field thereby increasing E E.
Electric Potential E E = kq 1 q 2 r V = E E q V = kq 1 r DE E = qdv Electric potential can also be measured a distance r from a main point charge q 1 ; note q 2 =q (ve test charge) Electric Potential Change in Energy (work done) in terms of the Potential Difference between any 2 points may also be calculated; NOTE: W = E E ; V is used for 1 pt. whereas V is between 2 pts.
Parallel Plates A B Special Case: parallel plates uniform ε If work is done to move a charge q from pt B to pt A then: W = Fd = qεd Since E E = W then qv = qεd and V = εd where d = r Electric Field: Decreasing potential
Parallel Plates e = DV r Note: Since e is uniform then DV r Units = V/m = J/C/m = N m/c m = N/C V if work is done to move a charge against the electric field This is for the magnitude of the electric field at any point in the space between two parallel plates a distance r apart with potential difference V The difference in potential energy per charge depends directly upon the charge s position in the field
Example 2 How much work must be done to increase the electric potential of a charge of 3.0x10 7 C by 120 V?
Example 3 The plate separation in a capacitor is 15x10 6 m. If a 9.0V battery is connected to the capacitor, what is the magnitude of the electric field intensity within the capacitor? *A capacitor is a twoterminal electrical component used to store energy in an electric field. It is used in electrical circuits.
Example 4 A small sphere has a charge of 3.0x10 6 C. Point X is located 60.0cm from the charge. a)find the electric potential at Point X. b)a charge of 2.0x10 6 C is placed at X. What is its electric potential energy? c)how much work was done in moving the 2.0x10 6 C charge from infinity to X?
Motion of Charged Particles in Electric Fields Consider 2 charges where q 2 is a main charge and q 1 is a smaller charge. If the charge is allowed to freely move, q 1 will move to the right due to the force of repulsion. It will accelerate to the right in the direction of the electric force as predicted by Newton s 2 nd Law. a = F E m But as the charge moves r, F E and a will too. the motion of a particle is difficult to analyse using Newton s Laws directly
Conservation of Energy in Electric Fields The total energy of the charges remains constant even though the distance between them changes. When q 1 is at r 1, q 1 is at rest so the total energy of the charged mass equals electric potential energy
Conservation of Energy in Electric Fields For 2 Like Charges: When charges move farther apart, E E is lost and becomes E K. E E = E K When you bring charges closer together, E K is lost and is stored as E E. E K = E E For 2 Opposite charges, the opposite happens.
Example 5 Find the speed of a 220 g puck on an air hockey table with a charge of 4.50 μc when it is 55.0 cm from a fixed puck of 5.20 μc charge if they are initially 18.0 cm apart.
Example 6 A TV has a potential difference of 2.0x10 4 V between its plates. Determine how fast an electron is travelling when it hits the screen.
EXTRA Shown is a simplified model of hydrogen. Calculate the electric work done in raising the electron from the ground state to the third orbital.