Physics 2e 18 and 19 Electric charge, electric field, electric potential and electric field
capacitors
* stores electric charge * has two metal plates that are not touching * charge from battery terminals seperates +/- into the two plates and stays there * the capacitor stays overall neutral in that circumstance * the capacitor is holding charge Q (Q_- + Q_+) * The amount of charge Q a capacitor can store depends on two major factors—the voltage applied and the capacitor's physical characteristics, such as its size.
T or F: charges move in an electric field and experience a change in electrical potential energy when doing so
*When charges move in an electric field, they experience a change in electrical potential energy, and this difference is associated with the voltage between two points in the field.
what coulombs law says about electric force
*as charge increases, the electric force increases *as distance increases, electric charge decreases *if more than 2 charges are present, vector analysis is required to find net force on any particle in system
electric potential (V) energy per unit charge
*potential energy per unit charge (PE/q) *independent of test charge q (stays the same regardless of magnitude of test charge) *potential difference (ΔV) between two points: ΔPE/q
electrical potential energy
*the amount of work required to bring some amount of charge from infinity. *positive charge wants to get to lowest potential, much like how a ball wants to roll down a hill. *Just as gravitational potential energy arises from the gravitational force between objects, electric potential energy arises from the electric force between charged particles. *Similar to gravitational potential energy, electric potential energy is a form of stored energy that can be converted into other forms of energy, such as kinetic energy or thermal energy, when the charged particles interact or move. *represents the potential energy stored in a system of charged particles due to their electric interactions *
voltage
- potential difference (change in potential energy between blah blah divided by the charge) - Equations: J/C | PE (or W)/q | 1V = 1JC^-1 - Voltage is not energy itself, but provides the potential for the movement of charge and the flow of electric current - Provides the potential for energy transfer
grounding
Completes an electric circuit and carries the current safely away. For our purposes, imagine a neutral earth. We put a negatively charged rod into the ground where the electrons flow into the earth. Then we sever connection to the earth, and have a positively charged rod.
represent electric potentials (voltages) pictorially
Consider Figure 19.8, which shows an isolated positive point charge and its electric field lines. Electric field lines radiate out from a positive charge and terminate on negative charges. While we use blue arrows to represent the magnitude and direction of the electric field, we use green lines to represent places where the electric potential is constant. These are called equipotential lines in two dimensions, or equipotential surfaces in three dimensions. Since the electric field lines point radially away from the charge, they are perpendicular to the equipotential lines.
total capacitance in parallel
Cp = C1 +C2 + C3 + ...
fundamental charge
1.6 x 10^-19 C
The magnitude of the elementary charge (carried by a single proton or electron), q, is... and represented by the subscript e indicates the charge of a single e- or p+
1.60 x 10^-19 Coulombs (q can be negative or positive depending on whether you're talking about a p+ or e-)
total capacitance in series
1/C1 + 1/C2 +1/C3 + ... question: why is it not just C + C + C...
Earth's Electric Field
150 N/C surrounds Earth, directed downward, with magnitude increasing as approach surface. Why? Ionosphere is 100km above the surface of Earth which contains a lot of charged particles. In fair weather the ionosphere is positive and the Earth is largely negative, maintaining the electric field.
1 coulomb is equal to _____.
6.25 x 10^18 charges
k in Coulomb's Law
9 x 10^9 N*m^2/C^2 assuming you're working with air as the surrounding. The value of K actually depends on the medium surrounding the charges.
can you create or destroy charge?
According to the law of conservation of charge, charge cannot be created or destroyed. Charge is a conserved quantity, which means that the total charge in a closed system remains constant over time. However, charge can be transferred.
Dielectric
An insulating material placed between the two plates of a capacitor, allowing for the storing of more charge (if the circuit is on) or a decrease in the voltage difference (if the circuit is off). The dielectrics can handle more electric field than can air before breakdown.
polar molecules reactions with electric forces
As opposed to nonpolar substances, polar substances have permanent dipole moments. In interaction with a field, the field can exert a force on the molecules dipoles. Similarly induced by the permanent dipole moments inherent within polar molecules are the ability to have dipole-dipole interactions and hydrogen bonding.
Capacitance for parallel plate capacitor
C = ɛ_0 · (A/d) ɛ_0 = 8.85 x 10^-12 F/m The constant ε_0 is the permittivity of free space; A = area d = distance between the two plates Units of F/m are equivalent to C^2/Nm^2
relationship: voltage and electric field
E = -ΔV/Δs *where Δs is the distance over which the change in potential, ΔV, takes place. The minus sign tells us that E points in the direction of decreasing potential. The electric field is said to be the gradient (as in grade or slope) of the electric potential.
the magnitude of the electric field for a point charge
E = k|Q|/r^2
electric field created by a point charge
E=kQ/r^2 An electric field is a region of space around a charged object where other charged particles experience a force
What happens if a conductor has sharp corners or is pointed?
Excess charges on a nonuniform conductor become concentrated at the sharpest points. Additionally, excess charge may move on or off the conductor at the sharpest points. The electrostatic repulsion of like charges is most effective in moving them apart on the flattest surface, and so they become least concentrated there. On a very sharply curved surface the charges are so concentrated at the point that the resulting electric field can be great enough to remove them from the surface. Smooth surfaces are used on high-voltage transmission lines, for example, to avoid leakage of charge into the air.
force between particles (coulombs law)
F = k(q_1 * q_2)/r^2
electric field (E) equation
F/q * where F is the Coulomb force * q is the test charge *it is understood that EE is in the same direction as FF. It is also assumed that q is so small that it does not alter the charge distribution creating the electric field. *measured in newtons per coulomb
T or F: polarization and induction are the same concepts, except polarization results in a temporary field while induction is typically more permanent or sustained
False - it is actually polarization that is quite permanent.
T or F: on the large scale, Coulomb forces tend to cancel, and that is because most objects are electrically charged and have net attractive and repulsive forces.
False. It is true that on the large scale, such forces tend to cancel (as opposed to gravitational force). That is because most objects are electrically neutral, or at least close enough, thus the + and - cancels out.
T or F: electrons can be viewed
False; electrons cannot be viewed, as they seem to be an infinitesimal point. They seem to be smaller than a wavelength of light. Also, consider Heisenberg's uncertainty principle. People have deemed electrons as having no internal structure or size in the classical sense.
work
Fdcosθ transfer of energy that occurs when a force is applied over a distance
why coulombs and newtons law are the same structure
First, we must highlight that the mathematical form of these laws can be understood through the concept of field theory. Similarly, they are both inverse squares in which the force is decreased as the distance between objects increases. Both equations of electric field and gravitational field follow the inverse square law, because the force of fields themselves follow the inverse square relationship with distance.
benefit, new constant, and equation associated with the addition of certain dielectrics to a parallel plate capacitor
In some instances the introduction of a dielectric can improve the amount of capacitance C that is possible with a capacitor. Thus, the new equation would be C = kɛ_0 · (A/d) There are charts to illustrate the k value for different dielectric materials
The movement of these ions through cell membranes is crucial to the motion of nerve impulses through nerve axons.
Na+, K+, and Cl-
electrostatic force and electric charge - are they the same concept?
No. Electrostatic force is the attraction (or repulsion) that arises between 2 charged objects, mathematically defined by Cuolomb's Law. Electric charge is a fundamental characteristic of matter.
electron volt
On the submicroscopic scale, it is more convenient to define an energy unit called the electron volt (eV), which is the energy given to a fundamental charge (e.g. electron) accelerated through a potential difference of 1 V. 1 eV = 1.60 x 10^-19
Microscopically, how does a dielectric increase capacitance?
Polarization of the insulator is responsible, and you may visualize the benefit of polar materials/molecules interacting with the Coulomb force. The Coulomb force between the closest ends of the molecules and the charge on the plates is attractive and very strong, since they are very close together. This attracts more charge onto the plates than if the space were empty and the opposite charges were a distance d away.
where do these charges come from?
Protons and electrons are the primary carriers of electric charge, in which electrons travel around the positively charged nucleus. Protons are located in the nucleus of an atom, while electrons orbit around the nucleus. When the number of protons and electrons in an atom is unequal, an electric charge is produced. Charges can also be transferred between objects through various processes like friction, conduction, or induction.
POTENTIAL DIFFERENCE
REFERS TO THE FORCE AND FLOW OF ELECTRONS IN AN ELECTRICAL CIRCUIT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IT IS CREATED BY A POWER SOURCE SUCH AS A GENERATOR OR BATTERY! ESTABLISHES A DIFFERENCE BETWEEN ITS TWO TERMINALS!!!!!!!!!!! VOLTS VOLT VOLTS !!!!!!!!!!!!!!!!! STUPID VOLTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Things with 1.60 x 10^-19
The magnitude of the elementary charge (carried by a single proton or electron) ... in Coulombs The Joules in 1 eV
why is dry table salt an insulator
The positive sodium ions and negative chloride ions are held together by strong electrostatic forces of attraction, forming a stable crystal lattice. This arrangement does not allow for the easy movement of ions.
Why do most objects tend to contain nearly equal numbers of positive and negative charges?
The reason is referred to as electrical neutrality in which a balance between positive and negative charges exists. In the absence of external influences, objects tend to have an equal number of positive and negative charges, resulting in a net charge of zero.
why electrostatic forces do not play a larger role in biology than they do if we have so many charged molecules.
The reason is that the electrostatic force is "diluted" due to screening between molecules. This is due to the presence of other charges in the cell. One might say that screening makes the Coulomb force a short range force rather than long range. since for example with H2O, a covalently bound molecule, the 2 dipoles terminate some of the electric field lines coming from a free charge such as on a DNA molecule
Faraday cage
This is a metal shield that encloses a volume. All electrical charges will reside on the outside surface of this shield, and there will be no electrical field inside. A Faraday cage is used to prohibit stray electrical fields in the environment from interfering with sensitive measurements, such as the electrical signals inside a nerve cell. During electrical storms if you are driving a car, it is best to stay inside the car as its metal body acts as a Faraday cage with zero electrical field inside.
T or F: The amount of energy transferred is related to both the voltage and the current flowing through the circuit.
True
T or F: One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor.
True; One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. This implies that a conductor is an equipotential surface in static situations. There can be no voltage difference across the surface of a conductor, or charges will flow. One of the uses of this fact is that a conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding. Grounding can be a useful safety tool. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the earth.
T or F: F_E >> F_g
True; electric force is 20 magnitudes greater than gravitational force
Van de Graaffs
Van de Graaffs utilize both smooth and pointed surfaces, and conductors and insulators to generate large static charges and, hence, large voltages.
For capacitors, specifically parallel plate capacitors, you can manipulate the 2 variables for a larger amount of capacitance. The results follow coulomb's law. What are the 2 variables?
We can see how its capacitance depends on A and d by considering the characteristics of the Coulomb force. We know that like charges repel, unlike charges attract, and the force between charges decreases with distance. So it seems quite reasonable that the bigger the plates are, the more charge they can store—because the charges can spread out more. Thus C should be greater for larger A. Similarly, the closer the plates are together, the greater the attraction of the opposite charges on them. So C should be greater for smaller d.
magnetic induction or electromagnetic induction (Induction)
What: process of generating a magnetic field in a material/object without physical contact. occurs when there is a change in the magnetic strength in a region of space. How: 1) when a magnet is moved relative to a conductor such as a wire the changing magnetic field induces a current in the conductor. This is the basis of electromagnetic generators and transformers. 2) changing an electric current through a conductor can induce a magnetic field around the conductor. This is the principle behind electromagnets. 3) inherently varying magnetic field itself can induce currents in conductive materials, such as alternating magnetic fields generating heat in cooking vessels. Why: power generation, transformers, wireless charging, data transmission.
importance of AT-REST conductors being at equilibrium or equipotential surface (no movement)
When a conductor is in electrostatic equilibrium, there is no net flow of charge within the conductor. An equipotential surface is a surface where all points have the same electric potential. In the case of a conductor, the electric potential is the same at every point on its surface. This means that there is no electric potential difference between different points on the surface of a conductor. If there were a potential difference across the conductor, charges would move along the conductor until they reached the region of lower potential, redistributing themselves until the potential becomes the same everywhere on the surface. In this state, the electric field inside a conductor is zero. The absence of an electric field inside the conductor ensures that charges remain stationary, creating a stable condition. So, while there may be a voltage difference across the conductor externally, the charges within the conductor redistribute themselves until the potential becomes the same at all points on the conductor's surface.
Is separating charges possible?
Yes, for example, by rubbing or by the electrochemistry in batteries. Rubbing materials together may have charges separate as one material (or molecules within the material) have a greater affinity for some said charge (some want more electrons, others give away). Chemical interactions may transfer respective charges to make the two terminals of a battery positive and negative (separate)
potential energy accounts for the work done by what kind of force?
a conservative force, such as gravitational potential energy or electric potential energy
Superconductor
a material that has almost zero resistance when cooled down, and moving electrons do not lose any energy (as opposed to typical conductors in which free electons can lose some energy due to collisions with molecules and atoms)
t or f: field lines can cross, the number of field lines leaving a pos or neg charge is not proportional to the magnitude of the charge, etc.
all false. Can't and is.
combination of capacitance leads to the total capacitance (in series)
capacitance of the combination is related to charge and voltage by C = QV
e
charge of a single electron in coulombs "The elementary charge"
the electrostatic force (Coulomb force) is (conservative/nonconservative), meaning what?
conservative; meaning work done on a charge, q, is independent of the path taken; that it is possible to define a potential energy associated with the force; and that change in PE is = -W or W=-ΔPE
defibrillator and capacitors
contains capacitors that can be adjusted, e.g. "adjust to 400 joules this time!" capacitors in general at uncharged are ΔV = 0. Charged ΔV = V
magnitude of the dipole
dipole moment
the number of field lines per unit area is exactly proportional to
electric field strength
E = k_c * q/r^2
electric field strength from a point charge
the gravitational force, another fundamental force, is actually sensed through
electromagnetic interactions of molecules between our feet and on the scale, for example
whenever a charged particle is created, another having an opposite charge is created with it always. Thus, total charge is again zero. They are matter-antimatter counterparts. An example is...
electrons and antielectrons aka positrons
holds dna together
electrostatic force Since the Coulomb force drops with distance (F ∝ 1/r2), the distances between the base pairs must be small enough that the electrostatic force is sufficient to hold them together.
quarks
elementary "point-like" particles (which electrons are, too) of matter that make up neutrons and protons. Quarks are believed to carry fractional charges. Protons and neutrons have 3 each. Proton - 2 up quarks, 1 down quark Neutron - 2 down quarks, 1 up quark
the charges of electrons and protons are
equal in magnitude yet opposite in direction
insulators
example: glass do not allow charges to move through them. Electrons and ions are bound in the structure and cannot move easily. They still move, but at a rate up to 10^23 times more slowly than in conductors.
T or F: unit of electrostatic force is newtons per Coulomb
false; that is the units for electric field.
action at a distance, aka forces that interact on objects without touching it, which occurs on objects at a distance more than a few atomic diameters, can be blamed on....
force field
T or F: free charges can be either positive or negative and are, in fact, positive in metals.
free charges are negative in metals.
difference between gravity and electrostatic forces
gravity is always attractive - electric forces can be + or -. A positive answer means repel, negative answer for coulombs law is an attractive force (I think?)
fast block
in reproductive fertilization, the egg cell membrane undergoes a depolarization event (wave of negativity) the moment it fuses with a sperm cell, which ensures that only a singular sperm cell can fuse with an egg cell. This is critical for embryonic development.
photoconductor
insulator when in dark, conductor when exposed to light. SELENIUM
static electricity
its effects are quantified by "electric charge" the force between charge decreases with distance
T or F: the coulomb force field surrounding any charge extends throughout space
its true but simplified. In reality, yes it would extend far and exponentially decrease, but would also be interfered with by its surroundings.
ELECTRIC POTENTIAL V OF A POINT CHARGE
kQ/r (point charge)
atomic and molecular interactions such as friction cohesion and adhesion
known to be manifestations of the electromagnetic force
conductor
material that has free electrons. Free electrons aren't bound to individual atoms or sites in the material, thus can move around rather free. examples: salt water, some metals
if we have an object with a known amount of net charge, can we predict how other electric charges will react when they pass nearby?
michael faraday says yes! He said electric fields permeate space and influence all charged particles. all charged things have a field.
there is no directly observed charge smaller than
q_e where q represents the charge of something, and e represents 1 proton or electron
polarization
separating electric charges, by perhaps using an external electric field. Creates internal positive and negative dipoles.
concept of a field
shows how an object can be acted on without direct contact within the field.
mechanical energy
sum of PE and KE
point charge Q and test charge q
test charge q is typically introduced in order to experimentally determine the magnitude and direction of a magnetic force field. Simply put, it measures the force of a field. point charge Q is an ideal concept where the field originates, and references a charge at a single point. NOTE: Electric field E is defined in such a manner that it represents only the charge creating it and is unique at every point in space.
T or F: opposite charge attracts because of the electric force
the electric force between two objects (given by Coulomb's Law) determines whether they will be attractive or repulsive. Negative result is attraction
Interestingly, whenever matter-antimatter counterparts are brought together, they completely annihilate one another. By annihilate, we mean...
the mass of the two particles is converted to energy E, again obeying the relationship Δm=E/c^2. This is because they are perfectly opposite charges and collide in a way that results in them cancelling each other's charge out. During the annihilation process the particles are converted from mass to energy as stated by Einstein's E=mc^2. Annihilation results in a release of photons or other things.
the total electric field created by multiple charges is
the vector sum of the individual fields created by each charge
T or F: electric charge is quantized
true
T or F: electrical potential V is scalar and has no direction
true
t or f an electric fields are vectors
true
t or f test charge q are positive, as to help determine the direction and magnitude of the electric field at different points in space, and so that the field lines point away from a positive charge and toward a negative charge.
true
T or F: charge is a conserved quantity, never to be violated
true, it is a special quantity similar to that of energy, momentum, and angular momentum
parallel plate capacitor
two identical conducting plates separated by a distance. When a voltage V is applied, the capacitor stores it as charge Q
farad
unit of capacitance
the field of two unlike charges compared to the fields of two like charges
unlike would be a weak field. between like, field is stronger since the fields for each charge are in the same direction and thus their strengths add.
charging by induction
without direct contact, a charge is manifested in a nearby object. Produces a temporary separation of charges via use of an external electric field.
relate energy to voltage
ΔPE = qΔV
