Chapter 19: Electric Potential & Potential Energy

Transcription

1 Chapter 9: Electric Potential & Potential Energy Brent Royuk Phys-2 Concordia University Terminology Two Different uantities: Electric Potential and Electric Potential Energy Electric Potential = Voltage Note: We will start by considering a point charge, section Electric Potential Energy Consider two point charges separated by a distance r. The energy of this system is U = kq oq r To derive this, you need to integrate work using Coulomb s Law. Potential energies are always defined relatively. Where is U = 0 for this system? What is negative energy? This is a scalar quantity. The Superposition Principle applies. We are most often interested in changes and differences, rather than absolutes. 3

2 Definition: Electric Potential V = U q o This is called the electric potential (which shouldn t be confused with electric potential energy), the potential, or the voltage. Remember: potential is energy per charge. Units In MKS, energy/charge = Joule/Coulomb = volt (V) In everyday life, what s relevant about this infinity stuff? Nothing, really. Potentials tend to be differences. One commonly chosen zero: the earth. 4 Comparisons An Analogy Coulomb Force --> Electric Field (Force per charge), as Electric Potential Energy --> Electric Potential (Energy per charge) How is electric potential energy similar to gravitational potential energy? Potential in this chapter compared to future chapters. 5 Electric Potential For a point charge, V = U q o = kqq o rq o = kq r 6 2

3 Electric Potential Examples A battery-powered lantern is switched on for 5.0 minutes. During this time, electrons with total charge -8.0 x 0 2 C flow through the lamp; 9600 J of electric potential energy is converted to light and heat. Through what potential difference do the electrons move? Find the energy given to an electron accelerated through a potential difference of 50 V. a) The electron volt (ev) An electron is brought to a spot that is 2 cm from a point charge of 2.5 µc. As the electron is repelled away, to what speed will it finally accelerate? Find the electric field and potential at the center of a square for positive and negative charges. What do positive and negative voltages mean? E-field lines point in the direction of decreasing V. 7 Electric Potential Examples How much work is required to assemble the charge configuration below? Electric Potential Examples Consider the three charges shown in the figure below. How much work must be done to move the +2.7 mc charge to infinity? 9 3

4 Potential in a Uniform Field Let s let an electric field do some work as we move a test-charge against the field: The work done by the field is: W = -q o Ed Assuming we start at the U = 0 point, we get U = -W = q o Ed Signs? See next slide. Using the definition of the potential we get: V = Ed 0 Potential in a Uniform Field Sign considerations: Work done by the field is negative, which makes the potential energy positive (useful). Compare with gravity: Potential in a Uniform Field 2 4

5 Potential in a Uniform Field Example: A uniform field is established by connecting the plates of a parallel-plate capacitor to a 2-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 µc moves from the positive plate to the negative plate. How much does its electric potential energy change? 3 Equipotential Surfaces An equipotential surface has the same potential at every point on the surface. Equipotential surfaces are perpendicular to electric field lines. The electric field is the gradient of the equipotential surfaces. How are equipotential lines oriented to the surface of a conductor? 4 Equipotential Surfaces 5 5

6 Equipotential Surfaces Comparative examples: Isobars on a weather map. Elevation lines on a topographic map. 6 Capacitors A plate capacitor It takes energy to charge the plates = CV C= Easy at first, then harder C is the capacitance Bigger C means more charge per volt, bigger charge storage device farad (F) = coulomb/volt εoa d εo = 8.85 x 0-2 C2/Nm2 (permittivity of free space) Connect with k What area plate separated by a gap of 0.0 mm would create a capacitance of.0 F? 7 Capacitors in Circuits Series Charge is same on all capacitors Voltage drops across the capacitors So V = V + V2 + V Since V = /C, C = C + C + C +... Therefore: eq Parallel Ceq = C + 2 C2 + 3 C The voltage is the same across all capacitors. Different amounts of charge collect on each capacitor = = CV, so CeqV = CV + C2V + C3V +... Generally, C = C + C + C +... eq

7 Dielectrics In real life, capacitor plates are not naked, the gap is filled with a dielectric material Dielectrics are insulators. Keeps plates separated, easier to build. Also increases the capacitance The dielectric constant Isolated capacitor: insert dielectric, E is reduced by /κ κ = the dielectric constant C = κc o 9 Dielectrics 20 Electrical Energy Storage Graph V vs. q: V Slope = /C What is the area under the curve? U = 2 V = 2 2C = 2 CV 2 2 7

8 Electrical Energy Storage A defibrillator is used to deliver 200 J of energy to a patient s heart by charging a bank of capacitors to 750 volts. What is the capacitance of the defibrillator? 22 8