Monday, December 6, 2010
Final solutions: problems 5-8, 5d
Friday, December 3, 2010
Review tomorrow: Saturday, 12:30 - 2:00 PM
Also, i added an additional final practice problem in the Transient Circuits Lab post below.
Photosynthesis: can you live with it?
I know some of you have mixed feelings about photosynthesis. You like the oxygen, but you are worried that a question about an oscillating electric field initiating photosynthesis might be bad for your health.
To the right is a poll regarding photosynthesis. What it asks about is how you would feel about a supplemental extra-credit question; so you wouldn't have to do it at all if you don't want to, and you could get extra credit if you did do it. It would focus on the physics part of photosynthesis --the very beginning, in which an electric field helps an electron get into an excited state
Here are my thoughts on the initial part of the photosynthesis process. The part where a “photon” is absorbed and an electron makes a quantum leap from its ground state to an excited state. I won't use the word photon, because: 1) we haven't defined that, and 2) it is actually not helpful for describing transitions or calculating their rates. I will describe the initiation of photosynthesis in terms of electric fields pushing on electric charges. These are things we have been studying this quarter.
An electric field comes from the sun. It propagates across millions of miles of empty space using the magic of induction to transform its energy into a magnetic form and then back again trillions and trillions of times. (This is the nature of light. It is composed of oscillating electric and magnetic fields.)
* This is the essentially a quantum measurement process and so it has a probabilistic aspect to it. You do not need to worry too much about that unless it is something that particularly interests you.
To the right is a poll regarding photosynthesis. What it asks about is how you would feel about a supplemental extra-credit question; so you wouldn't have to do it at all if you don't want to, and you could get extra credit if you did do it. It would focus on the physics part of photosynthesis --the very beginning, in which an electric field helps an electron get into an excited state
Here are my thoughts on the initial part of the photosynthesis process. The part where a “photon” is absorbed and an electron makes a quantum leap from its ground state to an excited state. I won't use the word photon, because: 1) we haven't defined that, and 2) it is actually not helpful for describing transitions or calculating their rates. I will describe the initiation of photosynthesis in terms of electric fields pushing on electric charges. These are things we have been studying this quarter.
At the Mg2+ site, before any light arrives, the electrons are sitting quietly in their ground state. This is a very stable state--a neon-like closed shell (2s2, 2p6). The electrons are quiet and happy. They see no reason to change.
An electric field comes from the sun. It propagates across millions of miles of empty space using the magic of induction to transform its energy into a magnetic form and then back again trillions and trillions of times. (This is the nature of light. It is composed of oscillating electric and magnetic fields.)
When the electric field, which has the wave-like form which we discussed in class, passes through the chlorophyll it exerts a force on the electrons in the Mg2+. One electron in particular will begin to oscillate due to the influence of the electric field wave. It moves up and down in the same way that a floating buoy in the ocean moves up and down when ocean waves pass by it. The force on the electron is given by qE(t), where q is the charge of the electron and E(t) is the electric field of the light wave.
In this oscillating phase, the electron is in a superposition state, in which it is partially in an excited state and partially still in the ground state. After a little while, the ligands began to notice this oscillating, partially excited electron. They grab for the excited electron. Their chance* of success is not 100%, but if they are successful they will spirit the excited electron away and use its energy to initiate a complex chemical and biological process (6H2O + 6CO2 --> …..).
From a physics point of view, the key step is the transfer of energy from the electric field to the electron. This occurs via the qE interaction which gets the oscillatory movement of the electron started. The force on a charge due to an electric field, qE, was one of the first things we learned about this quarter.
* This is the essentially a quantum measurement process and so it has a probabilistic aspect to it. You do not need to worry too much about that unless it is something that particularly interests you.
Thursday, December 2, 2010
Some things to consider in preparing for your final.
Here is a preview summary of what you could choose to focus on for the final. (I will add more later.) These will be the things that I will emphasize in composing the final. The purpose of the final is to help you solidify your understanding of the most important aspects of this class in a way that will enable you to remember them for longer than usual.
First, it is useful to be able to quickly sketch electric fields due to two or three charges. This sort of skill helps you visualize electric fields, for example, especially those emanating from an oscillating electric dipole which plays an important role in our understanding of electromagnetic radiation generation.
Second, you would wish to be able to analyze the currents and voltages (voltage differences) in simple circuits with a few resistors. In my opinion, the key to understanding circuits is to understand current. In a simple loop circuit, with no bifurcations, the current is and must be the same everywhere along the circuit path. Additionally, current divides and recombines at simple bifurcating junctions in a simple way: if the there is a bifurcation (fork) where in the upper half the resistance is 1 Ohm and in the lower half resistance is 2 Ohms, then the current through the upper half will be twice as large as the current through the lower half. This implies that two thirds of the total current goes through the upper half and one third through the lower half. If you understand this intuitively you'll be able to do every problem. You did not need any formula other than V=IR. V=IR tells you the voltage drop across any particular resistor in terms of I. Tto find the current, I, however, you need to analyze the entire circuit as a system. You cannot look at just one part and tell what I is. That is what it means to say that the current is a property of the entire system not of an individual part.
Third, think about circuits which include capacitors and inductors --can you confidently articulate the behavior of circuits with capacitors and inductors. We describe the behavior of circuits in three ways: with equations, with graphs, and with words. All three are important. I hope you will be comfortable with all 3 modes of communicating and understanding circuits.
Circuits with capacitors and inductors exhibit time dependence. Why is that? Think about that for a while. That is a good practice problem. Why do circuits with capacitors or inductors exhibit time-dependent? (There are two different answers, one for capacitors on for inductors. Feel free to post your thoughts on that here.)
Understanding LRC circuits is also a point of emphasis for us. Our focus, is on LRC circuits that are similar to LC circuits --the current oscillates, the charge on the capacitor oscillates -- however, they lose a little energy in each cycle. What part of the circuit causes that energy loss? How and when does it happen?
In general for LRC circuits, the key things to understand are: charge (in the capacitor), as function of time, current as a function of time, what their graphs look like, how to calculate them, and everything having to do with energy. Energy can be stored in some parts of the circuit --and you want to understand that and its time dependence. Energy can also be lost in one part of the circuit. Losing energy is a bit different from storing energy. Understand the rate of energy loss and how that relates to other things and how it adds up over time is a good thing.
Other things that are important to understand and remember include the essential nature of E&M radiation, how photosynthesis gets started, how an oscillating electric dipole can generate an electric field wave...
anything i have left out?
Your input. comments and questions are welcome.
First, it is useful to be able to quickly sketch electric fields due to two or three charges. This sort of skill helps you visualize electric fields, for example, especially those emanating from an oscillating electric dipole which plays an important role in our understanding of electromagnetic radiation generation.
Second, you would wish to be able to analyze the currents and voltages (voltage differences) in simple circuits with a few resistors. In my opinion, the key to understanding circuits is to understand current. In a simple loop circuit, with no bifurcations, the current is and must be the same everywhere along the circuit path. Additionally, current divides and recombines at simple bifurcating junctions in a simple way: if the there is a bifurcation (fork) where in the upper half the resistance is 1 Ohm and in the lower half resistance is 2 Ohms, then the current through the upper half will be twice as large as the current through the lower half. This implies that two thirds of the total current goes through the upper half and one third through the lower half. If you understand this intuitively you'll be able to do every problem. You did not need any formula other than V=IR. V=IR tells you the voltage drop across any particular resistor in terms of I. Tto find the current, I, however, you need to analyze the entire circuit as a system. You cannot look at just one part and tell what I is. That is what it means to say that the current is a property of the entire system not of an individual part.
Third, think about circuits which include capacitors and inductors --can you confidently articulate the behavior of circuits with capacitors and inductors. We describe the behavior of circuits in three ways: with equations, with graphs, and with words. All three are important. I hope you will be comfortable with all 3 modes of communicating and understanding circuits.
Circuits with capacitors and inductors exhibit time dependence. Why is that? Think about that for a while. That is a good practice problem. Why do circuits with capacitors or inductors exhibit time-dependent? (There are two different answers, one for capacitors on for inductors. Feel free to post your thoughts on that here.)
Understanding LRC circuits is also a point of emphasis for us. Our focus, is on LRC circuits that are similar to LC circuits --the current oscillates, the charge on the capacitor oscillates -- however, they lose a little energy in each cycle. What part of the circuit causes that energy loss? How and when does it happen?
In general for LRC circuits, the key things to understand are: charge (in the capacitor), as function of time, current as a function of time, what their graphs look like, how to calculate them, and everything having to do with energy. Energy can be stored in some parts of the circuit --and you want to understand that and its time dependence. Energy can also be lost in one part of the circuit. Losing energy is a bit different from storing energy. Understand the rate of energy loss and how that relates to other things and how it adds up over time is a good thing.
Other things that are important to understand and remember include the essential nature of E&M radiation, how photosynthesis gets started, how an oscillating electric dipole can generate an electric field wave...
anything i have left out?
Your input. comments and questions are welcome.
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