Study Guide

Electromagnetism Themes

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  • Particle Physics

    Gamma Ray Detectors

    There are a bunch of different kinds of fancy detectors that measure radiation. How do they work? Amongst many other things, they work by forming electric fields.

    The range of electromagnetic radiation is huge. And from gamma rays to radio waves, they all need detection from time to time, which is why we’ve made different kinds of detectors. We haven’t come up with one detector that could detect every kind of electromagnetic radiation, yet. We’re working on it.

    Gamma rays, which form the highest frequency portion of the electromagnetic spectrum, interact with matter (i.e. the detector) by three different processes: photoelectric absorption, Compton scattering, and pair production.

    The detector’s atoms become ionized by these super energetic photons called gamma rays. When that happens, primary charge carriers are created. These are just electron-hole pairs. When an electron is excited, moving to a new energy level in an atom, this looks just like a positive hole moving the other way.

    These fancy detectors are made with semi-conductors. Semi-conductors conduct electricity under certain conditions, but not others, as their name implies. Semi-conductors are atoms like germanium and silicon that are “lonely” and form solid crystals with their valence electrons.

    For example, germanium has 4 valence electrons and forms 4 covalent bonds7. If we bring a valence-5 atom next to it, then there’s an extra germanium electron now floating around, looking for a home. This is an n-type semiconductor.

    Similarly, bring a valence-3 atom next to germanium and now what– there’s an excess number of positive holes, which form acceptor states. This is a p-type semiconductor.

    That’s “n” for negative and “p” for positive. These physicists are pretty sneaky, huh?

    Bring an n-type and a p-type semiconductor together and we have a P-N junction, otherwise known as a diode, shown below.

    The center area contains the free electrons from the n-type semi-conductor which diffuse across the junction and into the p-type material. What happens then? Well, they combine with positive holes and get neutralized. The same thing happens for positive holes.

    What are we then with? A depletion region, which is just a region where charged ions are stuck since there are no mobile carriers, and we don’t mean cell service, but moving ions. Since these charged ions are made up of both positive and negative ions, they form…they form…? Yes, they form an electric field.

    Now, let’s go back to the gamma ray detector. Through the ionization of the germanium atoms, by photoelectric absorption, Compton scattering, or pair production, more electron-hole pairs are created in the atoms of the semiconductor. These electron-hole pairs drift under the influence of an external electric field towards their respective electrodes, where their motion is recorded as displacement current. This displacement current means an event occurred, which is what the detector is trying to, well, detect.

    Is that all?

    No. In an ideal world, this would be the end of it. We record the measured displacement current, which we translate as an event of gamma ray detection.

    Since an ideal world is fictitious, we have to consider an electron acting out of turn. What if an electron that’s part of the detector tries to sneak across the depletion region and into the forbidden land in secret? This is called leakage current.

    To minimize this scandalous behavior, physicists build gamma-ray detectors as reverse-bias diodes. These are P-N junctions, just as we’ve seen, except that the p-type material is connected to the negative terminal of a power supply, and vice-versa for the n-type material. This widens the depletion region such that in theory, any recorded current will be due to a gamma ray event.

    Observe a reverse-bias diode above, with the p-type holes attracted to the negative side of the battery and the n-type electrons attracted to the positive side. We can see why leakage wouldn’t occur to the electrons easily in this state. Unpictured is the ammeter measuring the current to watch for a gamma ray event.

    The low leakage current in a reverse diode may be further reduced by cooling the detector crystals to below 120 Kelvin, since low temperatures are synonymous with low energy, which robs electrons of the desire to “leak.”

  • Special Relativity

    Relativistic Electrodynamics

    Remember special relativity and its frames of references8? Where an event’s history depends on who we ask?

    Well, it happened. Special relativity reminds us that according to an observer, something could be at rest or moving depending on that observer’s own motion. An observer could perceive himself as being stationary in his own frame of reference, but he could still be whizzing through space at incredible speeds, but view space as the moving entity. That’s all well and dandy, but when a phenomenon, such as the formation of a magnetic field, depends on the motion of something, then we’ll probably start scratching our heads a little. Whose frame of reference do we use?

    A while back we learned how relativity alters fundamental notions such as time, energy, and momentum, and how no matter what, the laws of physics are the same in each frame of reference, though relating them to each other takes some skill. After all, Newtonian mechanics got quite the addition when Einstein came along.

    That’s all fine and dandy, but how do the fundamental notions of electromagnetism change, then, when taking into account special relativity?

    They don’t.

    Even Albert Einstein thought a lot about this: one of his famous papers is called On the Electrodynamics of Moving Bodies. Relativity says light is always traveling at speed c. What Maxwell’s equations say is that an electromagnetic wave in one frame of reference should still be an electromagnetic wave in another frame. Not only that, but all electromagnetic waves are traveling at speed . Always. No matter the frame of reference or speed of an observer: the speed of light is an absolute constant.

    Even electromagnetic induction relies on the relative motion of a magnet and a wire. It doesn’t matter which one is moving, as long as one of them does. This suggests no relativistic correction is needed for electromagnetic phenomena.

    This may be true, but there’s still a catch: although all components of electromagnetic fields obey Maxwell’s equations, which do not ever change, the electric and magnetic fields themselves can change depending on the observer. This may seem bizarre, but as we recall that a point charge creates an electric field while a current produces a magnetic field, we may start to catch the drift.

    Picture an observer sitting in the rest frame of a point charge and then start to move relative to it. In essence, according to the observer, there’s now a magnetic field present as well. What does it mean for the laws of electromagnetism to stay absolute? Simply that the electromagnetic field will break up consequentially in electric and magnetic components that are different for each observer.

    Pretty neat, huh?

    Brace yourself for a mind-blowing exploration of concept in Thoughts and Study.

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