Walker Chapter 202 Electric Potential and Electric Potential Energy Symbol for electric potential is V We will first define Electric Potential Energy. Symbol is U Scalar quantity (a magnitude, positive or negative, not a direction) Unit is Joule (J). Electric Potential Energy is an energy of a charged object in an external electric field. Electric Potential is the property of the electric field itself, whether or not a charged object has been placed in it.
Walker Chapter 203 The electrostatic force is a conservative force. Conservative because the force on a charge depends only on the position of the charge, not its velocity or past trajectory. We can define an electrical potential energy U (Joules) associated with the electrostatic force. Electrical Energy Terms and Definitions
Walker Chapter 204 As a charge q moves parallel (in same direction) to a constant electric field E, it experiences a force F=qE. The work done by the electric field is, W=Fd=qEd. (work is negative if force F and displacement d are in opposite directions) The change in the potential energy is just the negative of the work done by the electric field: U = - W = - qEd Electrical Energy Terms and Definitions (continued)
Walker Chapter 205 Change in electric potential energy Move the + particle opposite the direction of force = increase its potential energy
Walker Chapter 206 Question 1 A positive charge moves from a) to b) in the electric field E. The work done by the electrostatic force is: 1) Positive 2) Negative 3) zero (b) (a) W = F(x f -x i )
Walker Chapter 207 Question 2 A positive charge moves from a) to b) in the electric field E. The change in the electrostatic potential energy is : 1) Positive 2) Negative 3) zero (b) (a) U = Eq(x f -x i )
Walker Chapter 208 A uniform electric field of magnitude 4.1 x 10 5 N/C points in the positive x direction. Find the change in electric potential energy of a +4.1 µC charge as it moves from the origin to (a) (0, 6.6 m) [ans:0], (b) (6.6 m, 0) [ans:-11.1], and (c) (6.6 m, 6.6 m) [ans:-11.1] E Walker P. #1 q
Walker Chapter 209 It is often convenient to consider not the potential energy, but rather the potential difference between two points. The potential difference between points A and B, (V B -V A ), is defined as the change in potential energy of a charge q moved from A to B divided by that charge Potential is a scalar, NOT a vector. Electric Potential
Walker Chapter 2010 The potential V is measured in units of volts: 1 Volt = 1 V = 1 J /C = 1 N·m / C With this definition of the volt, we can express the units of the electric field as: [E]=1 N/C = 1 V/m Note: potential (V) potential energy (U) Unfortunately, we use V both for the electrostatic potential, and for its unit of measure, e.g. V(x 1 ) = 2.5 V. Units
Walker Chapter 2011 The zero of potential: For calculating physical quantities it is the difference in potential which has significance, not the potential itself. Therefore, we are free to choose as having zero potential at any arbitrary point which is convenient. Typical choices are: the earth infinity, i.e. remotely far from the charges we are studying. Electric Field, Electric Potential Energy, and Work U = W = -Fd V = U/q = Ed [1 N/C]=[1 V/m](uniform field)
Walker Chapter 2012 Energy Conservation A consequence of the fact that electric force is conservative is that the total energy of an object is conserved (as long as nonconserative forces such as friction can be ignored) Expressing the kinetic energy: Electric potential energy is
Walker Chapter 2013 Point Charges If we define the zero of potential to be at infinity, then the potential at a point A which is a distance r from a point charge q is found to have a potential given by: q A r (Dimensional analysis: E = kq/r 2, V has dimensions of E times a length. r is the only length in the problem).
Walker Chapter 2014 Many Charges and Superposition If we wish to know the potential at a given point in space which results from all surrounding charges, we simply add up the potential from each charge: Note that because potential is a scalar, the summation is less difficult than for the vector field E. If we have a continuous distribution of charge, we use techniques of integral calculus to calculate V(x,y,z).
Walker Chapter 2015 Potential and Work For any group of charges, we can calculate the work done by the electrostatic force as the charges are brought together from infinity. The potential energy associated with a two charge system: q1q1 q2q2
Walker Chapter 2016 Walker P. #33 The three charges are held in place in the figure below, where L = 1.25 m. (a) Find the electric potential at point P [ans:76.9 kV] (b) Suppose that a fourth charge, with a charge of 6.11 C and a mass of 4.71 g, is released from rest at point P. What is the speed of the fourth charge when it has moved infinitely far away from the other three charges? [ans:14.1 m/s]
Walker Chapter 2017 It is often convenient to work with a unit of energy called the electron volt. One electron volt is defined as the amount of energy an electron (with charge e) gains when accelerated through a potential difference of 1 V: 1 eV = (1.6 · 10 -19 C)V= 1.6 · 10 -19 J The Electron Volt (eV) A Battery is an electron pump. A battery (1.5 V), each electron pumped through the battery from + to - is given a potential energy of 1.5eV.
Walker Chapter 2018 A (real or imaginary) surface in space for which the potential is the same everywhere is called an equipotential surface. The electric field at every point on an equipotential surface is perpendicular to the surface. Equipotential surfaces are like contour lines on a topographic map. Equipotential Surfaces
Walker Chapter 2019 Electric Field Lines and Equipotential Surfaces for two point charges (Electric field lines and Equipotential surfaces are always mutually perpendicular).
Walker Chapter 2020 Q A capacitor is device that stores the energy associated with a configuration of charges. In general, a capacitor consists of 2 conductors, one with a charge +Q and the other with a charge –Q (on the surfaces). Any geometry is a capacitor Capacitance + + + + + -
Walker Chapter 2021 The capacitance C is defined as the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between the conductors: For parallel plate C = A 0 /d. (C does not depend on Q or V) [V = Ed, E=Q/(A 0 ), V = Qd / (A 0 )] The unit of capacitance is the Farad (F):1 F = 1 C/V
Walker Chapter 2022 The Parallel-plate Capacitor A common type of capacitor is the parallel-plate capacitor, made up simply of two flat plates of area A separated by a distance d. Its capacitance is given by: where 0 is a constant called the permittivity of free space. 0 =8.85 10 -12 C 2 / Nm 2
Walker Chapter 2023 A dielectric is an insulating material in which the individual molecules polarize in proportion to the strength of an external electric field. This reduces the electric field inside the dielectric by a factor , called the dielectric constant. Capacitance is increased by . and Dielectrics For fixed charge Q on plates
Walker Chapter 2024 Dielectric Strength Dielectrics are insulators: charges are not free to move (beyond molecular distances) Above a critical electric field strength, however, the electrostatic forces polarizing the molecules are so strong that electrons are torn free and charge flows. This is called Dielectric Breakdown, and can disturb the mechanical structure of the material
Walker Chapter 2025 Dielectric Properties of common materials MaterialDielectric Constant: Dielectric Strength (V/m) Vacuum12.5·10 18 Air (lightening)1.00059 ( -1) Density 3.0·10 6 Teflon2.160 ·10 6 Paper3.7 16 ·10 6 Mica5.4100 ·10 6
Walker Chapter 2026 Energy Stored in a Capacitor Recall that work is required to move charges about or “charge” the capacitor. The work required to charge a capacitor with a charge q to a voltage V is: So this must correspond to the energy stored in the capacitor. Because Q=CV, this can be rewritten:
Walker Chapter 2027 Walker P. #50 (a) What plate area is required if an air-filled, parallel-plate capacitor with a plate separation of 2.8 mm is to have a capacitance of 26 pF? [ans:0.00822 m 2 ] (b) What is the maximum voltage that can be applied to this capacitor without causing dielectric breakdown? [ans:8.4 kV]