29 30 1 SJP draft Magnetism 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 Efields 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 1 In fact all magnets seem to have 2 sides or poles Once you ve labeled the poles you ll notice they act like this 1 2 1 Attract 2 Opposite poles attract and like poles repel 1 2 2 2 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 N impossible N You always have called a dipole magnet because it has two different poles N S If you break a magnet you DON T get one N only and one S only magnets instead you simply get two smaller N S N S dipole magnets 1 29 30 2 SJP draft 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 N S 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 N S 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 S N 29 30 3 SJP draft 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 29 30 4 SJP draft 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 Side view top view Current I B The B field lines form CIRCLES around the wire or current x I stronger weaker The direction of the Bfield is found with the B 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 29 30 5 SJP draft 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 Side view B top view x x I x x x x I x B x B x I x x x x x 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 B I B 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 B x absolutely need RHR 1b but I just I find it much quicker and easier when you have current loops to deal with Which we will often 29 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 some external B field the current is …
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