Simple Nature - Light and Matter

figure h/1, which implies the existence of induction effects. Butthis example involves circular motion, so it doesn’t quite work as away of proving that induction exists. When we say that motion isrelative, we only mean straight-line motion, not circular motion.A more ironclad relativistic argument comes from the arrangementshown in figure i. This is also a generator — one that isimpractical, but much easier to understand.Flea 1 doesn’t believe in this modern foolishness about induction.She’s sitting on the bar magnet, which to her is obviously at rest. Asthe square wire loop is dragged away from her and the magnet, itsprotons experience a force out of the page, because the cross productF = qv × B is out of the page. The electrons, which are negativelycharged, feel a force into the page. The conduction electrons arefree to move, but the protons aren’t. In the front and back sides ofthe loop, this force is perpendicular to the wire. In the right andleft sides, however, the electrons are free to respond to the force.Note that the magnetic field is weaker on the right side. It’s asthough we had two pumps in a loop of pipe, with the weaker pumptrying to push in the opposite direction; the weaker pump loses theargument. 8 We get a current that circulates around the loop. 9 Thereis no induction going on in this frame of reference; the forces thatcause the current are just the ordinary magnetic forces experiencedby any charged particle moving through a magnetic field.Flea 2 is sitting on the loop, which she considers to be at rest.In her frame of reference, it’s the bar magnet that is moving. Likeflea 1, she observes a current circulating around the loop, but unlikeflea 1, she cannot use magnetic forces to explain this current. As faras she is concerned, the electrons were initially at rest. Magneticforces are forces between moving charges and other moving charges,so a magnetic field can never accelerate a charged particle startingfrom rest. A force that accelerates a charge from rest can only bean electric force, so she is forced to conclude that there is an electricfield in her region of space. This field drives electrons around andaround in circles, so it is apparently violating the loop rule — it isa curly field. What reason can flea 2 offer for the existence of thiselectric field pattern? Well, she’s been noticing that the magnetici / A generator that works withlinear motion.8 If the pump analogy makes you uneasy, consider what would happen if allthe electrons moved into the page on both sides of the loop. We’d end up witha net negative charge at the back side, and a net positive charge on the front.This actually would happen in the first nanosecond after the loop was set inmotion. This buildup of charge would start to quench both currents due toelectrical forces, but the current in the right side of the wire, which is driven bythe weaker magnetic field, would be the first to stop. Eventually, an equilibriumwill be reached in which the same amount of current is flowing at every pointaround the loop, and no more charge is being piled up.9 The wire is not a perfect conductor, so this current produces heat. Theenergy required to produce this heat comes from the hands, which are doingmechanical work as they separate the magnet from the loop.Section 11.5 Induced Electric Fields 689