Electric Potential and Electric Potential Energy

1. Electric Potential and Electric Potential Energy PAP Physics Mrs. Martin

2. Electric Potential Energy • The amount of energy associated with an electric field • Just as with gravitational potential energy

3. Work in a uniform electric field • Always assume movement from the positive plate (area of high potential) to a negative plate (area of low potential) (Remember the convention is that we are always analyzing a positive charge) • So moving a positive charge from the negative plate toward the positive plate results in negative work and a positive change in potential energy • Moving a negative charge from the negative plate toward the positive plate results in a positive work but a negative change in potential energy

4. Electric potential • Change in electric potential energy per charge • As you move from one place to another • A positive charge moves naturally from an area of high potential to an area of low potential. • A negative charge does exactly opposite • ∆V = ∆U/q = -W/q • V = Electric Potential (V) • U = Potential Energy (J) • q = Charge within the field (C) • W = Work (J) • A common unit of energy is an electron Volt (eV) • 1 eV = 1.60 x 10-19J

5. Zero potential point • The zero potential point is chosen arbitrarily, just as it was when discussing gravitational potential energy. • Some typical voltages • Thundercloud to ground 108 V • High voltage power line 106 V • Household outlet 102 V • Flashlight battery 1.5 V

6. Energy Conservation • The total energy of the charge is conserved • Ki + Ui = Kf + Uf • Remember K = ½ mv2 • Positive charges accelerate in the direction of decreasing electric potential • Negative charge accelerate in the direction of increasing electric potential

7. Example • Suppose an electron in a picture tube of a television set is accelerated from rest through a potential difference of 5000V. (a) What is the change in potential energy of the electron? (b) What is the speed of the electron as a result of this acceleration? What if we used a proton?

8. Electric Field and Electric Potential • E = V/d • E = Electric Field (V/m) • V = Electric Potential (V) • d = distance (m) • Notice that Electric Field can also be measure in V/m • 1N/C = 1 V/m

9. Example • A uniform electric field is established by connecting the plates of a parallel-plate capacitor to a 12 V battery. (a) If the plates are separated by 0.75 cm, what is the magnitude of the electric field in the capacitor? (b) A charge of +6.24 x 10-6 C moves from the positive plate to the negative plate. Find the change in electric potential energy for this charge.

10. The Electric Potential of Point Charges • The electric field is said to be zero infinitely far from a given charge • Formula • V = kq/r • V = Potential Difference (V) • Can be + or – dependent upon the charge • k = electric constant • q = charge causing the electric field (C) • r = distance from the charge (m)

11. Electric Potential Energy between two charges • Formula • U = q0V = kq0q/r • U = Potential Energy (J) • q0 = charge experiencing field (C) • k = electric constant • q = charge causing field (C) • r = distance from field (m) • Example • Find the electric potential produced by a point charge of 6.80 x 10-7C at a distance of 2.60 m.

12. Superposition of Electric Potentials • The total electric potential due to two or more charges is equal to the algebraic sum of the potentials due to each charge separately. • Potential difference is a scalar quantity and therefore the sum is simple adding or subtracting potential differences based on charges.

13. Example • A charge q = 4.11 x 10-9C is placed at the origin, and a second charge equal to -2q is placed on the x axis at the location x = 1.00m. (a) Find the electric potential midway between the two charges. (b) The electric potential vanishes at some point between the charges; that is, for a value x between 0 and 1.00 m. Find this value of x.

14. Equipotential Surfaces • Any point on a contour has the same electric potential and any other point on the same contour. • The electric field always points in the direction of decreasing electric potential • The electric field is always perpendicular to the equipotential surfaces

15. Capacitors and Dielectrics • Capacitor • Stores electric charge and energy • Two plates separated by a finite distance • When connected to a battery, on plate becomes charge +Q and the other –Q • The greater the amount of Q, the greater the capacitance

16. Capacitance • Formula • C = Q/V • C = Capacitance (farad, F) • Q = Charge of the plate • V = Potential difference between the plates • Example • A capacitor of 0.75μF is charged to a voltage of 16V. What is the magnitude of the charge on each plate of the capacitor?

17. Parallel Plate Capacitor • Simplest of capacitors • Capacitance is dependent upon the area of the plate and the distance between them • Formula • C = ε0A/d • C = Capacitance (F) • ε0 = 8.85 x 10-12 c2/(N•m2) permittivity of free space • A = Area of the plates (m2) • d = distance between plate (m)

18. Parallel Plate Capacitor, Cont. • Example • A parallel-plate capacitor is constructed with plates of area 0.0280 m2 and separation 0.55mm. Find the magnitude of the charge on each plate of this capacitor with the potential difference between the plates is 20.1 V. • Capacitance increases with Area • Capacitance decreases with distance

19. Dielectrics • Insulating material inserted between the plates of a parallel plate capacitor. • Example: Keyboard • Increases the capacitance of the capacitor • Decreases the electric field between the plates by a value of k • k = dielectric constant (different for different materials) • This also decreases V between the plates, which increases C

20. Dielectrics, cont. • Formula • C = kε0A/d • C = Capacitance (F) • k = dielectric constant • ε0 = constant • A = Area (m2) • d = distance between plates (m)

21. Example • A parallel-plate capacitor is constructed with plates of area 0.0280 m2 and separation of 0.550 mm. The space between the plates is filled with a dielectric with a dielectric constant of k. When the capacitor is connected to a 12.0V battery, each of the plates has a charge of 3.62 x 10-8 C. What is the value of k?