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CU-Boulder PHYS 1120 - Magnetism

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32-1 (SJP-phys1120) 1 2 1 2 1 2 Attract 1 2 2 1 RepelMagnetism: In 1110 and 1120 so far we’ve seen 2 fundamental forces of nature: gravity and electrical forces. Electrical force depends on the existence of charge – charges make E fields, and then E fields in turn exert forces on other charges, F = qE. There is another kind of force in the world, called magnetism (attracting “rocks” were found in Magnesia > 2,000 years ago). You’ve surely played with kitchen magnets. They stick to some materials but not others. E.g. magnets don’t stick to aluminum. Magnetism is not equal to Electricity! They are different forces! E.g.: Hold a magnet near the electroscope (which is very sensitive to even tiny amounts of electric charge). Nothing happens! E.g.: Hold a magnet near those electric dipole seeds we used to demo E-fields. You’ll see nothing. E.g.:Charge up a balloon, hold a magnet near it. Nothing. Magnetic forces are new, a different force than electrostatics. Phenomenology of Magnets: Play with magnets a little! Some attract, and some repel. In fact, all magnets seem to have 2 “sides” or “poles”. Once you’ve labeled the poles, you’ll notice they act like this: Opposite poles attract and like poles repel: This is a bit like electricity, where we also had two charges: opposites attracted while likes repelled. But this is not electrical! So let’s avoid naming the magnetic “charges” + and -. Here’s another name: “N” and “S” (North and South). We’ll label one (arbitrarily) and then we can figure out all the others in the world. Unlike electricity, you’ll never see: You always have called a "dipole" magnet, because it has two (different) poles. If you break a magnet, you DON'T get one "N-only” and one "S-only" magnets, instead you simply get two smaller dipole magnets! N S N N S SN (impossible) N32-2 (SJP-phys1120) There is a magnetic field which (like E-fields) extends through space. It exerts a force on other magnetic objects. (It’s a vector associated with every point in space) We can use little “test magnets” to map out a B field (just like little “test charges” mapped E-fields for us.) E.g. Iron filings, or a small compass, near a magnet. The compass can define the direction of those lines. We can draw arrows on field lines (pointing where the compass does). (Looks rather like an electric dipole E-field pattern!) Remember, opposites attract, and a compass needle’s tip is (by definition) “N”, so the compass points towards (is attracted to) the “S” pole of other magnets. The Earth is a giant magnet: A compass points towards the geographic “North” of the planet, so the magnetic “S” pole (of the giant hidden magnet) sits up near the planet’s geographic N pole! (It's a little strange, think about this picture until you understand the conventions) N S N S N S32-3 (SJP-phys1120) Some key questions to ask now:  What makes/causes magnetic fields (call them B-fields)?  Can we quantify the strength of B-fields?  Can we quantify the effects of B-fields? Lots of experiments were done (1800’s) to figure this out. E.g.: 1) (Oersted discovered) B-fields are always created by currents, i.e. by moving electrical charges! (So although B-fields and E-fields are very different, they are also related too) 2) B-fields always exert forces on any other currents. So what about regular magnets? (Where’s the current in a kitchen magnet? You don’t need to buy batteries for them, right?!) Answer: All atoms have tiny currents around them, all of the time! (Just the electrons in orbit.) But normally, atoms are randomly oriented, so there’s no net effect. (Magnetic fields of different atoms cancel) But if the atomic currents all line up (which happens only in unusual and special materials, like ferromagnets!) then they act magnetic. This happens in E.g. iron (Fe), Nickel, Cr, not too much else. + -32-4 (SJP-phys1120) The “rules” of magnetism we’re about to discuss cannot be derived, they are experimental facts. They look crazy, in fact, but this is how the world apparently works! Rule #1: Given a current, what is the B field? Currents (I) always spontaneously form B-fields around themselves. (Compare with the old rule “ charges make E-fields around themselves”) We'll discuss the formula for the strength of B in a few pages. But for now, lets just look at the pattern: The B field lines form CIRCLES around the wire (or current) The direction of the B-field is found with the Right Hand Rule #1. (RHR1): Take your right thumb, point it along the current direction, I . Your fingers naturally curl around the current the same direction B does. (Try it, see if you understand the directions in the pictures above) Note: the pictures are meant to be 3-D. I use a standard convention: • means the field is pointing AT you (out of the paper) X means the field is pointing AWAY from you (into the paper). To remember this, I sometimes think of the X as saying “dig here, buried treasure.” Other people think of an arrow. If it points towards you, you only see the tip. If it’s running away from you, you see the tail feathers... X (stronger) B x • Current, I (weaker) Side view top view • B I32-5 (SJP-phys1120) Example: A current flows around a ring (a loop). What does the B field look like? Answer: We can't yet exactly derive the answer, but you can see it intuitively just from the previous rule. Think about the B field produced by little pieces of the wire, and then imagine “superposing” them, building up the total B field. Here’s my sketch - think about it a little, does it make any sense to you? Look again at this figure. Some people introduce another “Right Hand Rule” for this situation, which we might call “Right Hand Rule #1b” RHR1b: To find the B field near a current loop, rather than a long wire: If your right hand fingers curl with the current in a current loop, your thumb points in the direction of the B through the center of the loop. This is different than the RHR#1 (where your thumb pointed with I, and your fingers pointed like B! ) So don’t mix them up! You never absolutely need RHR #1b, but I just find it much quicker and easier when you have current loops to deal with. (Which we will, often.)


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CU-Boulder PHYS 1120 - Magnetism

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