EXAM 2 CHs (#24,25,26) Review Guide
Learning Objectives After reading this module, you should be able to ... 25.1.1 Sketch a schematic diagram of a circuit with a parallel-plate capacitor, a battery, and an open or closed switch. 25.1.2 In a circuit with a battery, an open switch, and an uncharged capacitor, explain what happens to the conduction electrons when the switch is closed. 25.1.3 For a capacitor, apply the relationship between the magnitude of charge q on either plate ("the charge on the capacitor"), the potential difference V between the plates ("the potential across the capacitor"), and the capacitance C of the capacitor.
Chapter 25 learning objectives
The Electric Force is ____________ and therefore has an associated potential energy.
Conservative
Convert Energy between units of Joules and ________________.
Electron - Volts
The electric potential at any point on the central axis of a uniformly charged disk is given by ____________, Starting with this expression, derive an expression for the electric field at any point on the axis of the disk.
Eq. 24.5.7
The SI unit for capacitance
Farad (F)
Explain how Gauss' law is used to find the capacitance of a parallel-plate capacitor.
Gauss' law is a powerful tool in electromagnetism that relates the electric field to the charge distribution. It states that the flux of the electric field through a closed surface is proportional to the charge enclosed by that surface. In the context of a parallel-plate capacitor, Gauss' law can be used to find the electric field between the plates, and this, in turn, can be used to find the capacitance. Consider a parallel-plate capacitor with a plate area A, plate separation d, and a charge Q distributed uniformly on the plates. We can imagine drawing a cylindrical Gaussian surface between the plates, with one endcap on one plate and the other endcap on the other plate, and the curved surface of the cylinder perpendicular to the plates. By Gauss' law, the flux of the electric field through this surface is equal to the charge enclosed by the surface, which is Q. The electric field E between the plates is perpendicular to the plates and has the same magnitude at every point between them. The electric field lines are straight and parallel, pointing from the positive plate to the negative plate. Therefore, the electric field E is given by:
In a region that is completely filled by a dielectric, all electrostatic equations containing the permittivity constant must be modified by replacing ε₀ (the permittivity of free space) with ε (the permittivity of the dielectric material). This is because a dielectric material has the ability to polarize in the presence of an electric field, which reduces the effective electric field in the material and increases the capacitance of any capacitors in the region. The permittivity of the dielectric material is a measure of its ability to store electric charge in an electric field and is related to the permittivity of free space by a factor known as the dielectric constant (κ). Thus, the new permittivity constant in the presence of the dielectric is ε = κε₀.
Key Idea regarding the permittivity of free space by a factor known as the dielectric constant (K).
A given device (conductor, resistor, or any other electrical device) obeys __________ _____ if its resistance R, defined by Eq. 26.3.1 as V/i, is independent of the applied potential difference V. A given material obeys Ohm's law if its resistivity, defined by Eq. 26.3.3 is independent of the magnitude and direction of the applied electric field .
Ohm's law
Sample Problem 25.6.1 Dielectric partially filling the gap in a capacitor Figure 25.6.2 shows a parallel‐plate capacitor of plate area A and plate separation d. A potential difference V0 is applied between the plates by connecting a battery between them. The battery is then disconnected, and a dielectric slab of thickness b and dielectric constant κ is placed between the plates as shown. Assume A = 115 cm2, d = 1.24 cm, V0 = 85.5 V, b = 0.780 cm, and κ = 2.61. (a) What is the capacitance C0 before the dielectric slab is inserted?
Sample Problem 25.6.1 Part I
Sample Problem 25.6.1 Part II
Sample Problem 25.6.1 Part II
Sample Problem 25.6.1 Part III
Sample Problem 25.6.1 Part III
_________________ are materials that have few conduction electrons but can become conductors when they are doped with other atoms that contribute charge carriers.
Semiconductors
_______________________ are materials that lose all electrical resistance at low temperatures. Some materials are superconducting at surprisingly high temperatures.
Superconductors
If a particle with charge q is placed at a point where the electric potential of a charged object is V, the electric potential energy U of the particle-object system is
U = qV
Drift Speed of the Charge Carriers When an electric field is established in a conductor, the charge carriers (assumed positive) acquire a drift speed νd in the direction of ; the velocity is related to the current density by
Where ne is carrier charge density
The SI unit of electric current is the __________________________
ampere (A): 1 A = 1 C/s.
The proportionality constant C is called the _________________ of the capacitor. Its value depends only on the geometry of the plates and not on their charge or potential difference. The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them: The greater the capacitance, the more charge is required. The SI unit of capacitance that follows from Eq. 25.1.1 is the coulomb per volt. This unit occurs so often that it is given a special name, the farad (F): (25.1.2) As you will see, the farad is a very large unit. Submultiples of the farad, such as the microfarad (1 μF = 10-6 F) and the picofarad (1 pF = 10-12 F), are more convenient units in practice.
capacitance
If a charged particle moves through a ______________ in electric potential without an applied force acting on it, relate ____ and the _____________ in the particle's _________________.
change ΔV, ΔV, change ΔK, kinetic energy
When a circuit with a battery, an open switch, and an uncharged capacitor is completed by closing the switch, _____________ ___________ shift, leaving the capacitor plates with ____________ charges.
conduction electrons, opposite
If a charged particle moves from an initial point to a final point in an _______________________________ , apply the relationships between ____________________ in the potential, the _______________ , the ________________ in the potential energy, and the work W done by the electric force.
electric field, change ΔV, particle's charge q, change ΔU
Identify that in every charged objects electric field, the object sets up an _____________ which is a ____________, that can be positive or negative depending on _____________ .
electric potential V, scalar quantity, the objects charge
If a charged particle moves through a change ΔV in ________________________ while an ___________________________________ , relate ΔV, the change ΔK in the particle's kinetic energy, and the work _________ done by the applied force.
electric potential, applied force acts on it, Wapp
When a dielectric material is placed in an _________ electric field, it develops an ___________ electric field that is oriented opposite the external field, thus reducing the magnitude of the electric field inside the material.
external, internal
Inserting a dielectric into a capacitor causes _____________ _____________ to appear on the faces of the dielectric and weakens the electric field between the plates.
induced charge
The ____________ ________ is less than the free charge on the plates.
induced charge,
The entire conductor, including ____________ points, is at a _____________________________.
interior, uniform potential.
If an isolated conductor is placed in an external electric field, then at every ________ point, the electric field due to the ________ electrons cancels the ________ electric field that otherwise would have been there.
internal, conduction, external
If the space between the plates of a capacitor is completely filled with a dielectric material, the capacitance C in vacuum (or, effectively, in air) is multiplied by the _____________ ____________ __________ ____, which is a number greater than 1.
material's dielectric constant κ
Also, the _____________________ at every point on the surface is _____________ to the surface.
net electric field, perpendicular
For a charged particle placed at a point in an objects electric field, apply the relationship between the _____________ at the point, ________________, and ______________________ of the particle object system.
object's electric potential V, the particles charge q, and potential energy U
An excess charge placed on a conductor will, in the equilibrium state, be located entirely on the ________________________ of the conductor.
outer surface
If a charged particle moves between two given points in the electric field of a charged object, identify that the amount of work done by the electric force is __________________________.
path independent
capacitor consists of two isolated conductors (the plates) with charges +q and -q. Its capacitance C is defined from _ _ __ where V is the potential difference between plates.
q = cv
Electric potential is a ____________ not a _____________
scalar, vector
The electric potential V at a point P in the electric field of a charged object is
A. ("where W∞ is the work that would be done by the electric force on a positive test charge q0 were it brought from an infinite distance to P, and U is the electric potential energy that would then be stored in the test charge-object system".)
