Commons

charge, there will be magnetic fields. Because there is a largenumber turns in the coils, these fields are fairly strong, and storequite a bit of energy.When you pull the plug, the circuit is no longer complete, and thecurrent stops. Once the current has disappeared, there’s no moremagnetic field, which means that some energy has disappeared.Conservation of energy tells us that if a certain amount of energydisappears, an equal amount must reappear somewhere else.That energy goes into making the spark. (Once the spark is gone,its energy remains in the form of heat in the air.)We now have two connections between electric and magneticfields. One is the principle of induction, and the other is the ideathat according to relativity, observers in different frames of referencemust perceive different mixtures of magnetic and electric fields. Atthe time Faraday was working, relativity was still 70 years in thefuture, so the relativistic concepts weren’t available — to him, hisobservations were just surprising empirical facts. But in fact, therelativistic idea about frames of reference has a logical connectionto the idea of induction.Figure x is a nice example that can be interpreted either way.Observer A is at rest with respect to the bar magnets, and seesthe particle swerving off in the z direction, as it should accordingto the right-hand rule. Suppose observer B, on the other hand, ismoving to the right along the x axis, initially at the same speedas the particle. B sees the bar magnets moving to the left and theparticle initially at rest but then accelerating along the z axis in astraight line. It is not possible for a magnetic field to start a particlemoving if it is initially at rest, since magnetism is an interaction ofmoving charges with moving charges. B is thus led to the inescapableconclusion that there is an electric field in this region of space, whichpoints along the z axis. In other words, what A perceives as a puremagnetic field, B sees as a mixture of electric and magnetic fields.This is what we expect based on the relativistic arguments, but it’salso what’s required by the principle of induction. In B’s frame ofreference, there’s initially no magnetic field, but then a couple ofbar magnets come barging in and create one. This is a change inthe magnetic field, so the principle of induction predicts that theremust be an electric field as well.Electromagnetic wavesTheorist James Clerk Maxwell was the first to work out the principleof induction (including the detailed numerical and geometricrelationships, which we won’t go into here). Legend has it that itwas on a starry night that he first realized the most important implicationof his equations: light itself is an electromagnetic wave,a ripple spreading outward from a disturbance in the electric andmagnetic fields. He went for a walk with his wife, and told herx / Observer A sees a positivelycharged particle movesthrough a region of upwardmagnetic field, which we assumeto be uniform, between the polesof two magnets. The resultingforce along the z axis causes theparticle’s path to curve toward us.y / James Clerk Maxwell (1831-1879)Section 6.3 Induction 127