Sunday, July 31, 2011

On the Sources of Magnetic Fields

The topic this meeting is far far ahead of the topics that we have in Lecture class, so everything was quite new to me (but thinking about it, I don't think I'd learn anything in Lecture class if we discussed this :|). So basically, this meeting was all about the sources of magnetic fields, of which there are a number of.

The first source is permanent magnets, or the objects that naturally have a magnetic field associated with them. Basically that's it for permanent magnets.

The second source is the motion of charged particles, which is given by the equation:

where B=magnetic field vector, v=velocity vector, mu-knot=permeability of free space, q=charge of the moving particle, r=unit vector from position of particle to point where B is measured

This complicated equation basically says that the magnetic field is the cross product of the velocity and position vector wrt to where it is being measured times a constant given by the other terms. This means that there is no magnetic field when the velocity and position vectors lie on the same line (cross product is 0) while it is a maximum when the two vectors are perpendicular.

An extension of this source of magnetic fields is a current carrying wire. I won't put the equation anymore because I can't find a picture of it in Google, but I would say that the equation is quite similar in form to the one stated above.

Another source is a very long solenoid. When I first heard of this word, I was quite clueless of what it is. I previously heard of it in Physics 111 when we were discussing the divergence of a vector field. It was said that a solenoidal vector field is one that has 0 divergence at all points. I had no idea of what it meant, and still no idea at present. :| What I do know is how a solenoid looks like. It's basically a wire curled up to resemble a compressed slinky. This source of magnetic field also has an equation associated with it. Here:

Okay, I now want to talk about the experiment that we performed. Just like the other experiments that we had, this experiment is also a series of 'mini' experiments about the sources of magnetic fields.

The first mini experiment that we performed was measuring the magnetic field at different points around a permanent magnet (horseshoe and bar) using a magnetic field sensor and labquest. Honestly speaking, this part was quite arduous because the measurements were quite erratic and we had to take a LOT of measurements.

Then, the next thing that we did was to measure the magnetic field from the center of a horseshoe to the outside part of the horseshoe. Okay, that was quite confusing. Basically, we measured the magnetic field as a function of distance from the horseshoe.

We, then, proceeded to perform the next mini experiment. Here, we made use of iron fillings placed on top of a folder. Under the folder, a horseshoe magnet was used, and the iron fillings aligned themselves according to the magnetic field produced by the magnet. It was quite cool because it was like magic.

We were supposed to do Oersted's experiment. Well, actually, we did but it failed. So we had to scrap it off from the procedures list.

Then, we did the final mini experiment, which was to measure magnetic field outside a solenoid which carried a current. We, then, implemented different core materials and looked at how it affected the magnetic field.

... So that's all that we did this meeting.

The experiment was very long and tiring. We were there by 1 and ended at 4, making use of the full 3 hours this meeting. Initially, I thought that the experiment would be fast. But, boy, I was wrong. I haven't fully grasped the concepts of magnetic fields, so I don't know if our data makes any sense. Well, hopefully they do.:))

It's amazing how people (physicists) discovered how magnetic fields work, and even derived equations that explain how they occur. I'd never had known any of these if I didn't enter Physics.

I was also amazed by the device Labquest. I want one for my own.:D

Sunday, July 24, 2011

On Kirchoff's Rules and Capacitors, the Return

The whole meeting this week was dedicated to answering a relatively long quiz about our previous two experiments.

The quiz was implicitly divided into two parts: one on Kirchoff's and the other on capacitance. The first set of items on Kirchoff's Rules were quite easy, because it just demanded from us knowledge on how to use the equations of Kirchoff's Rules. But it was a bit of a struggle for me to get the right answer because of wrong arithmetic. Roar.

The second set of items on Kirchoff's Rules required of us deeper thinking. And this is where I was sweating bullets because it was quite difficult.

The capacitance part of the exam was easy, relative to the part on Kirchoff's Rules. We were given the equations of the charge and current. The only thing that we needed to do was to plug in values. :D

Needless to say, this quiz was a challenge for me, but what made it tolerable was the fact that Mac helped me out and that Sir Baldo was there, available if help was needed.

After the exam, Sir Baldo returned to us our lab notebooks. He told us that we were given a chance to revise our not-up-to-par lab notebooks so that we would have a higher score. :D

Thursday, July 21, 2011

On Trials and Tribulations

My blog post this meeting is short, primarily because we didn’t conduct an experiment.

Anyway, this meeting was dedicated solely for reviewing the coverage of our long exam (which by now is already two days past). Needless to say, the review was very useful and informative. Some selected items in our problem sets were answered live by sir, which made me go “ah” a few times because of the fact that some items were easier watching being answered than answering them myself. Sir was also kind enough to provide a copy of the answers to us. Thanks Sir! ^_^

Some thoughts on the exam:

ü The exam was excruciatingly HARD. (I don’t know if others had a hard time as well)

ü I think I failed the exam.

ü I hope the checker is generous in giving partial scores.

I guess I’m not really cut out to be someone great at electromagnetism. One exam down, three more to go. I hope I don’t fail the other exams.

Saturday, July 9, 2011

On Kirchoff's Rules and Capacitors

This meeting was quite hectic because two activities were scheduled to be done by 4 pm so that we wouldn't have to perform any experiment next meeting, and we could just review for our long exam in 102, which I consider my impending doom.

Anyway, the lab meeting started with a lecture on Kirchoff's rules and Capacitors, two very new concepts for me. Because of the possible lack of time, the quiz on these topics was postponed to next next week (yey!).

So, the first topic for the lecture was Kirchoff's rules, which are basically two rules on how to simplify measuring current and voltage in a DC circuit.

The first rule, the junction rule, states that "the algebraic sum of the currents at any branch point or junction in a circuit is zero." This rule fortunately conforms to common sense, so "getting" it isn't really that hard. For example, in the situation where a junction connects three branches and two currents (I1 and I2) are flowing into the junction, th
e current flowing out of the junction is I1+I2. Basically, the junction rules says that the sum of the directed currents in a junction is equal to 0. It is, in disguise, the Law of Conservation of Charge.

The second rule, the loop rule states that "the algebraic sum of the potential differences around any complete loop in the network is zero." This is a bit more difficult to grasp qualitatively than the junction rule, nevertheless, it's still a lot easier to understand than the things we learn about in 102 and 111. To put it simply, the voltage input and output must equal zero for any loop in the circuit. After reading a bit about it in University Physics, using the loop rule seems a bit complicated when the loop involves a lot of circuit elements.

The second part of the lecture was about capacitors and capacitance, a new addition to 102.1's ever growing collection of circuit elements.

The marking C is the capacitor in the circuit, and the unit of capacitance is farads. Before going in deeper on capacitors, let me first define it. Capacitors are devices which can store charge, and capacitance is just the measure of how much charge a capacitor can store. The amount of charge stored is determined by
where Q=charge, C=capacitance, V=voltage

The capacitance C is given by another formula:
where E=permitivity of free space, A=area of the plate of capacitor, d= distance between capacitor plates

When there is an insulator between the plates of the capacitor, the capacitance C becomes:
where k is a constant of the insulator that is very much greater than 1

We, then, described the effective capacitance in series and parallel circuits. For series, the capacitance formula is equivalent to that of the resistance formula for parallel circuits. For parallel, the formula is equivalent to that of the resistance formula for series.

The charge obtained by the capacitor and circuit current, as functions of time, was derived via integration. The formulas are:
q(t)=CV(1-1/e^(t/RC)) ----> charging (charge)
i(t)=V/(Re^(t/RC)) ----> charging (current)
q(t)=Q/e^(t/RC) ----> discharging (charge)
i(t)= -Q/RCe^(t/RC) -----> discharging (current)

Wow, those were a lot of formulas.:o

Anyway, we started doing the experiments after the lecture. The first we performed was the experiment on Capacitors. The first thing that popped into my mind when I saw the capacitors was that they seemed awfully familiar. I remember very vaguely that we handled capacitors in HS, but I do not know what we did with them.

The experiment on Capacitors was basically a string of activities that, in one way or another, displayed the wonders of capacitors. I do not want to go much into detail but as an outline, what we did are as follows:
  • dissected a capacitor (which was quite difficult)
  • measured the capacitor's capacitance (with the ever-powerful multimeter)
  • measured the capacitance for series and parallel combinations
  • made an experiment that proved the equation Q=CV
  • energized a capacitor and connected it to a voltmeter that was connected to a computer and by using labpro (which was cool), graphed the time vs voltage plot
There was a lot of sources of confusion for this experiment. One of which is our lack of knowledge on capacitors. I, for one, do not know a great deal about capacitors, and I consider myself an amateur when it comes to circuits. The last mini activity was confusing because there was a lot of things involved, and the procedure stated in the activity sheet didn't really go much into detail of what we were supposed to do. Thank God Sir was there, kind enough to help us out.

Lab Pro was really cool because it not only allowed us to get the graph of time vs voltage, but it also allowed us to get a best fit curve of the graph. For the first part of the graph (charging up until the capacitor was fully charged), the graph resembled an inverse exponential function. For the second part of the graph (after turning off the power supply/ discharging the capacitor), the graph resembled a natural exponential function.

By 3:40, we were done with the Capacitor experiment. With only a few minutes left until 4:00, we had to rush the Kirchoff's Rules experiment.

Around this time, too, I saw who I thought was Mikaela Fudolig entering the room looking for our instructor. I was :O and very starstruck (Mac was too) because Mikaela Fudolig is amazing. Having that high of a graduating GWA (1.099) at a young age (16), with her course being Physics to boot, I consider her very inspiring and cool.

I digressed. So, back to the experiment. It was quite a short experiment. We just set up a circuit given a diagram and just measured the voltage, current and resistance. By using Kirchoff's rules, we then solved for the current passing through each element... actually, we didn't do the last step there because it was already past 4. So, we just did it at home.

These two quickfire experiments were quite difficult for me because it required of us to be fast workers, so that we would finish by 4. Knowing myself, my motto in these kinds of experiments is 'work slowly, but surely'. Needing to finish 2 experiments in a span of 2 hours, my motto was thrown out of the window.

It's nice to have groupmates that are very much knowledgeable on circuits. After class, I can ask things that I did not understand during the course of the meeting. For example, using the breadboard was still quite vague to me. I can ask help from Mac after class and after that, I'm enlightened quite a bit.

So, I plan to read on the topics that we have discussed and will discuss, and hopefully by next next week, I will be a master of circuits. :D

Sunday, July 3, 2011

On Resistance and Resistors

For the first time of the semester, Mac and I were late in Physics 102.1. We had to finish the paper and make the final touches so that it would be great, but it seemed that time eluded for me and my group mate. Being tardy was quite saddening because of one reason stated later in the blog, but at least it imposed on my mind the mentality that I should NEVER be late again for 102.1.

So, for the aforementioned reason, when Mac and I entered the classroom, class had already begun and two questions in our prelab quiz were already given out. When I found out about that, I panicked because two questions in, the thoughts of failing the quiz lingered in my mind. I am not good at circuitry, and even if I studied the snippets of info on resistance in our guide sheet, I don't think I "got" what I had to know for the quiz. Thank God Sir Baldo made the quiz do-able. I only managed to get a 6/10 because I exchanged the relationship between I(total) and I(in the circuit) between series and parallel circuits. These activities (and attendance etc.) constitute 5% of our grade, so I need to up my game when it comes to these quizzes to get a decent mark... So no more being late for me!:D

The experiment this meeting was basically a compilation of "mini" experiments focused on the concepts of resistance, and consequently, resistors. Resistance is basically the ratio between voltage and current, as stated in Ohm's Law R=V/I, or in layman's terms, the measure of opposition to an electric current. Resistors, on the other hand, are devices that provide resistance to a circuit. The resistance of a sample (resistor included) is given by the equation:
where: R= resistance, p= resistivity, L=length of sample, A=cross sectional area
It was also stated that resistivity is temperature dependent. That is, at higher temperatures, resistivity increases, thus, the resistance of a sample increases.

I am not going to go into the details of the experiments that we conducted but simply give a breeze-through of what we did and what I thought about them.

The first thing we did was to measure the resistance of ceramic resistors via their bands and comparing it with the values that we got when we measure their resistance via an ohmmeter. This activity was very easy because it just required basic reading skills and simple arithmetic. To add to that, we did this in High School, which I really can't say regarding the other activities that we performed.

The second thing was finding out the schematic diagram of a resistance box. Initially, we thought that the circuit was simply a series because removing we didn't really understand how the mechanism worked. After consulting with Sir, we found out that removing the plugs actually increased the resistance and thereby there were resistors looped around each plug. It was very confusing for me because my knowledge on circuits is rusty. And the next activities just proved that more.

The third and fourth things were to find out the maximum resistance of a rheostat and a variable resistor. Initially, we thought that the rheostat increased its resistance with increased force of push.Regarding the variable resistor, we had no idea. Again, with consultation from Sir, we found out that the position of the sliding thing on the rheostat dictated the resistance because it served as a shortcut for the current to get to the other side. For the variable resistor, the same idea was concerned, though it was still confusing for me.

The fifth thing was measuring the resistance of two resistors connected in series and in parallel. This activity made use of a breadboard, and it was the very first time I've ever seen something like it. I was O_O when I saw it because I didn't know such a thing existed in this world. So, we put the resistors on the breadboard and took their resistance. We, then, solved the theoretical resistance using the bands and Ohm's Law. There was little percent error associated but they were small enough to be ignored.

The last thing that we did was circuit analysis for both ohmic and non-ohmic cases. Here, we made use of a power supply to give out voltage and an ammeter to take the current reading.For the ohmic case, we just made use of a ceramic resistor. For the non-ohmic case, a tungsten lightbulb. The obvious difference between the two cases is the pattern of the data. For the ohmic case, it was very much linear, but for the non-ohmic, the pattern was a bit eccentric but the trend was also increasing.

Admittedly, I wasn't really that useful this meeting because of my lack of knowledge on the topic. I know that it's my responsibility to know about the subject matter beforehand, but this week was very busy for me to fully prepare. To add to that, our Lecture class isn't really helpful at all because the lessons there are far behind the subject matter in Lab. It could possibly be an advantage because it implies that I would be prepared for the future topics in Lecture because we have already taken up in class.

As time goes on, I am beginning to realize that I am more of a mathematician than a physicist. It's very hard for me to grasp the concepts of electromagnetism because I can't imagine stuff that well, but numbers and equations make sense to me. Still, I want to continue on with Physics because maybe I haven't really exerted that much yet to "get" the topics. I think I can succeed if I try harder... And that is I being optimistic.