sign in sign up
<<
Home , Electric field

List of important topics: • Charge • • Electric • () • sources (potential difference, conductors) • • Ohm’s law • Circuits (series, parallel, diagrams, overloading) • Power • Poles N,S • Fields • Materials (iron, regions) • Currents è Magnets • E çè M (, meters, motors) • E çè M induction (Faraday’s law: E field induced by changing B) • Generators, alternators • Power production • Tranformers • E çè M B field induced by changing E

Week 9

Next period

General E&M theory • fields • Electric • Magnetic • relationship (electromagnets è an effect that links these 2 forces

Fundamental Electric Forceè Coulomb’ law • charges • attraction repulsion • !!∗!! • � = � � !! o depends inversely on the distance squared o depends on the magnitude of each charge o signs of the charges determine direction o force is a vector o direction is shown as � [called a unit vector] !!∗!! o � is used to calculate the magnitude or strength of the force !!

We want to understand that there is a fundamental view of nature that establishes what matter is and how matter interacts. These underpinnings are theoretically supposed to explain much of what we see and experience. However, it is extremely difficult to calculate general phenomena directly from first principles. Scientists have developed steps that start at the basic tenets and then show that they are valid for simple systems. The approach is then to extract the fundamental and critical parts and apply them in the form of a model. The result is a valid description at all levels that stems from the basic tenets but is not a direct calculation of the behavior. For example: Most chemists use molecular and atomic models that predict chemical behavior. The idea of covalent and ionic bonding along with some other ingredients suffices to make very powerful predictive tools. The actual fundamental calculation using positively charged cores (nuclei) surrounded by negatively charged interacting through the E&M force is intractable. A problem that can be solved is the hydrogen that consists of only 2 particles. This system has been studied and calculations match theory at a precision of 1ppm. This is a clear verification that the underlying theory is a good approximation to reality and extrapolations to should be able to model complex systems by extracting and applying the key elements of the theory. It is important to understand this hierarchy in science. Models based on our understanding of basic principles but employing simplifications and extracting critical factors are the trademarks of science. No one expects to predict cell behavior by using particle . However, cell behavior should never violate conservation of .

Fundamental theory: • Matter consists of groupings of elementary particles. The current list of particles that seem to exhibit this label (elementary or fundamental) are: electrons, quarks (u,d), muons ….. • Our world is primarily made from quarks that combine to produce protons and . Electrons, protons, constitute the basic building blocks for much of what we experience. Although protons and neutrons are not really fundamental because they are composite systems of quarks. the internal nature doesn’t reveal itself for most matter and is irrelevant to the majority of chemistry and material properties in which we are interested. {We did discuss carbon dating and of isotopes. To understand these processes we do need to consider the quark make up of the neutron. In this class knowing that isotope decay via radioactive processes suffices. No understanding of the underlying theory is expected.} • Matter interacts via 4 fundamental forces or interactions: o gravity ( and distance) o E&M (charge, motion of charge, distance) o Weak (responsible for neutron decay, not usually relevant) o Strong (hold protons and neutrons in closely packed arrays as nuclei) So to understand why books are supported on a table and why we can live in an atmosphere filled with material (air), we recognize that are the basic structures of matter. • Atoms consist of a nucleus surrounded by electrons. The negative electrons are bound to the positive nuclei primarily due to the electric force of attraction between charges. o Atoms are labeled by the number of protons in the nucleus o Isotopes are nuclei that have the same number of protons but different numbers of neutrons. o Usually only one isotope is stable and therefore remains unchanged while other isotopes eventually transition to the stable form. § Discussed C14 and C12 as an example of isotopes and described how carbon dating is achieved by measuring the loss of C14 due to its decay. • Atoms combine to make . The electric force is still the essential ingredient in understanding formation. [ is also essential for our understanding of molecules and atoms but we will not need to worry about these details.]

Electricity E&M is a complex . This interaction is responsible for most of the features we experience in our world. Basis for atoms and molecules. Determines material properties and interactions. Most phenomena (excluding gravity, falling and earth-sun-moon binding) can be seen as an E&M interaction. 2 charges +,- N,S è - , No individual N or S poles found Protonè + , made of quarks Due to electric currents  q q Same characteristics as electric force 1 2 ˆ F = k 2 r r only for N,S poles drops with distance act along line joining charges like repel, unlike attract € r=distance between charges rˆ = unit vector it shows direction only q q k 1 2 = provides magnitude of force, r2 sign € + means repulsion, neg means attraction

€ While originally the interactions in the columns appeared similar they were considered to be distinct, unrelated interactions. However, the forces were linked when electric currents were found to have magnetic interactions (electromagnet).

Electric current Measured in Amps A Flow Amount of charge that passes through an imaginary slice in a wire per second 1 A = 1 C/s Analogs: water flows in rivers (flowè amount passes by per second Flow of cars on highway (flowè # cars pass under bridge per second Therefore flow depends on two quantities speed, amount Few cars traveling fast = high flow Many cars traveling slow high flow Flow at 2:00 AM (90 MPH) i.e. the # under the bridge in a given time can be the same as the flow for a traffic jam (1 MPH). Mississippi can have slow moving sections where the river is wide and faster sections where the river is narrow but the flow is the same.

Voltage Push that causes the flow Analog: For rivers flow is due to gravity è Flowing down hill Analog: For skiers its due to gravity (vertical drop) Analog: Gravity can be used to propel material along a path the amount of push can be related to the height h. In trying to understand voltage we can consider things that flow down hill due to gravity. We can also identify the height that a skier descends or a river traverses as an important factor in determining flow. Indeed we can imagine that voltage can be directly linked to the height for a system that has material flowing due to gravity. This link allows us to develop some intuition about voltage and voltage distribution in a circuit.

Students are not required to know the details of Maxwell’s equations or the general force law as shown in the following aside. Aside è Fundamental structure of E&M Maxwell's equations are a set of partial differential equations that, together with the law, form the foundation of classical electrodynamics, classical optics, and electric circuits.     F = qE + qv × B Lorentz force Formulation in terms of total charge and current, differential form SI UNITS € Name Differential form

Gauss's law

Gauss's law for magnetism

Maxwell–Faraday equation (Faraday's law of induction)

Ampère's circuital law (with Maxwell's correction)

Formulation in terms of total charge and current, form SI UNITS Name Integral form

Gauss's law

Gauss's law for magnetism

Maxwell–Faraday equation (Faraday's law of induction)

Ampère's circuital law (with Maxwell's correction)

.

A qualitative understanding of each law is important and provided below.

Define the field in terms of the force experienced per unit source     General force law è F = qE + qv × B Lorentz force. For we can see the field is the force per unit charge.  F E = q € The test charge should not be moving in orde r to eliminate interactions with the . €

Gauss’s law There is a force between electric charges that satisfies Coulomb’s E law (with the Lorentz Force)

Gauss’s law Same for magnets (no fundamental monopoles) B Faraday A changing magnetic field induces and electric field. A equation pushed and pulled through a loop of wire drives a current around the loop. Since there are no monopoles there is no “magnetic analog of current”. All N, S are ultimately created by moving electric charge so fundamental fields are generated ultimately by electric charge. Ampere’s -Currents produce magnetic fields law with -Changing electric fields produce magnetic fields. .

Field- Let us take the definition of the field and find the field at some points,

Postive point charge Electric field

Parallel plate (plates must be large compared to the gap)

Magnetic field of a wire (What field does an electric current generate ß Ampere’s Law

Magnetic field of a loop Magnetic field of a coil

N-S dipole field Several loop coil field Electric charge moving in a circular path can produce a similar “external” field as that due to a N-S dipole. So to build a actual bar magnet we can line up a set of small loops (atoms)

For a magnetic material you can align the atoms. These atoms need to have some overall rotating charge that can be considered as a loop. The combined movement of all the electrons in an atom does not always create such a pattern but if it does then the atom possesses a magnetic dipole field. If you can line up these small there sum will be a large dipole (bar magnet). Permanent magnets have these dipoles aligned without external fields. The mechanism that keeps regions aligned to form permanent magnets is called ferromagnetism. ASIDE (not important) ferro, dia, para are the three ways materials can behave magnetically. For ferromagnets, at short distances, the exchange interaction (Pauli exclusion) is much stronger than the dipole-dipole magnetic interaction. As a result, in a few materials, the ferromagnetic ones, nearby spins tend to align in the same direction. In simple terms, the electrons, which repel one another, can move "further apart" by aligning their spins, so the spins of these electrons tend to line up.

The plastic block with filings suspended in liquid provides a visualization of the field.

Energize a coil of wire we see that it behaves like a N-S bar magnet. This demonstrates what the pictures above show.

Electric charges attract/repel they are the source of electric fields. N,S poles attract and repel and show a similar but different force, the magnetic force. Moving charges create magnetic fields (attract and repel N, S poles) and are moved (pushed or pulled) by magnetic forces. There are no fundamental N,S poles but the way moving charges behave they act almost in the same way that N,S poles behave. However the simplest configuration (loop) possesses 2 poles a N and a S pole. If N,S are simply a manifestation of moving charge there will always be a N_S combination and there is no way to create an isolated effective N or S pole. The fields E, B are also linked because a changing E or B produces a B or E. This is easy to demonstrate for the case of changing B. The complementary relation changing E creates B is critical to the nature of the fields but is not so easily demonstrated nor does it become essential when evaluating many applications. However it is critical to the understanding of and how energy in the form of the E and B fields can move. This explains how light reaches us from the sun and how cell phones can launch your messages to your colleagu