29_30-1 (SJP-draft)1 2 1 2 1 2 Attract 1 2 2 1 RepelMagnetism: In 1110 and 1120 so far we’ve seen 2 fundamental forcesof nature: gravity and electrical forces. Electrical force depends on theexistence of charge – charges make E fields, and then E fields in turnexert forces on other charges, F = qE. There is another kind of force inthe world, called magnetism (attracting “rocks” were found in Magnesia> 2,000 years ago). You’ve surely played with kitchen magnets. Theystick to some materials but not others. E.g. magnets don’t stick toaluminum. Magnetism is not equal to Electricity! They are differentforces!E.g.: Hold a magnet near the electroscope (which is very sensitive toeven 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, becauseit 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 smallerdipole magnets! N S N N S SN (impossible) N29_30-2 (SJP-draft)There is a magnetic field which (like E-fields) extends through space. Itexerts a force on other magnetic objects. (It’s a vector associated withevery point in space)We can use little “test magnets” to map outa B field (just like little “test charges”mapped E-fields for us.)E.g. Iron filings, or a small compass, near amagnet.The compass can define the direction ofthose lines. We can draw arrows on fieldlines (pointing where the compass does).(Looks rather like an electric dipole E-field pattern!)Remember, opposites attract, and acompass needle’s tip is (by definition) “N”,so the compass points towards (is attractedto) 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) sitsup near the planet’s geographic N pole!(It's a little strange, think about thispicture until you understand theconventions) N S N S N S29_30-3 (SJP-draft)Some key questions to ask now:ν What makes/causes magnetic fields (call them B-fields)?ν Can we quantify the strength of B-fields?ν 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-fieldsare 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 kitchenmagnet? 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 nonet effect. (Magnetic fields of different atoms cancel)But if the atomic currents all line up (which happens only in unusual andspecial materials, like ferromagnets!) then they act magnetic.This happens in E.g. iron (Fe), Nickel, Cr, not too much else. + -29_30-4 (SJP-draft)The “rules” of magnetism we’re about to discuss cannot be derived, theyare experimental facts. They look crazy, in fact, but this is how theworld 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 justlook at the pattern:The B field lines formCIRCLES around thewire (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, buriedtreasure.”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 I29_30-5 (SJP-draft)Example: A current flows around a ring (a loop). What does the Bfield look like?Answer: We can't yet exactly derive the answer, but you can see itintuitively just from the previous rule. Think about the B field producedby 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 HandRule” 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, yourthumb 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, andyour fingers pointed like B! )So don’t mix them up! You neverabsolutely need RHR #1b, but I justfind it much quicker and easier whenyou have current loops to deal with. (Which we will, often.) B x I Side view top view B I I B x x x x x x x x x x x x x x I I B B B29_30-6 (SJP-draft)Rule #2: Given a B field, what force does a current feel?B-fields exert a force on currents. If you put a current I into
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