What Is the Use of a Newborn Baby?

By the early 1800s, Oersted, Ampere and others had firmly established that moving charges, currents, produce magnetic fields. A natural question followed almost immediately: does the reverse also work? Can a moving magnet produce an electric current? Around 1830, Michael Faraday in England and Joseph Henry in America answered this, independently and conclusively, with yes. In Faraday's first experiment, a coil is connected to a galvanometer, and a bar magnet's north pole is pushed toward it: the galvanometer needle deflects, but ONLY while the magnet is actually in motion, returning to zero the instant it stops, even while held right up against the coil. Pull the magnet away, and the needle deflects again, but in the OPPOSITE direction; using the south pole instead reverses both deflections; and pushing or pulling the magnet faster produces a noticeably larger deflection. Replacing the magnet with a second, current-carrying coil produces exactly the same pattern, current is induced in the first coil only while the second coil is in relative motion toward or away from it, confirming it is genuinely the RELATIVE motion between magnet and coil, not the magnet's strength alone, that matters. A third experiment removed motion from the picture entirely: two stationary coils, one connected to a galvanometer, the other to a battery through a switch. Pressing the switch produces only a brief, momentary deflection, as the second coil's current (and field) rises from zero to its steady value; holding the switch down produces nothing further, since the current is now constant; releasing the switch produces another brief, opposite deflection, as the current falls back to zero. Something changing, not something merely present, however strong, is what these experiments hold in common.

Before Faraday's own law can be stated precisely, it needs a well-defined quantity to describe how much magnetic field passes through a surface, exactly the same role electric flux played back in electrostatics. For a flat area A sitting in a uniform field B, the magnetic flux through it is ΦB = B.A = BA cosθ, where theta is the angle between the field and the area's own normal direction; for a field that varies in strength or direction across a surface, the same idea extends to a sum over many small area elements, ΦB = the sum of Bi.ΔAi over the whole surface. Magnetic flux is measured in weber (Wb), equivalently tesla-metre-squared, and, like electric flux, is a plain scalar, no direction of its own. Faraday's genuinely great insight was recognising a single, simple mathematical relationship tying his experimental observations together: an emf is induced in a coil precisely when the magnetic flux through it changes with time, and the SIZE of that induced emf equals the rate of that change, ε = -dΦB/dt. For a closely-wound coil of N turns, where the same flux threads through every turn, the total induced emf multiplies accordingly: ε = -N dΦB/dt. Since flux depends on three separate quantities, field strength B, area A, and orientation angle theta, changing ANY one of them, moving a magnet to change B, stretching or shrinking a coil to change A, or rotating a coil to change theta, is equally capable of inducing an emf; Faraday's experiments happened to vary B, but the law itself is entirely indifferent to which of the three is actually changing.

Faraday's law gives the SIZE of an induced emf but leaves its direction to a minus sign; German physicist Heinrich Lenz supplied the missing rule in 1834: the induced current always flows in whichever direction opposes the very change in flux that produced it. Push a bar magnet's north pole toward a coil, and the flux through the coil increases; the induced current then flows in exactly the direction needed to generate its OWN magnetic field opposing that increase, which works out to a north pole facing the approaching magnet's north pole, repelling it. Pull the magnet away instead, and the flux decreases; now the induced current reverses, creating a south pole that faces the receding magnet, attracting it back. In both cases, the induced effect actively resists the change, never helps it along. This is not an arbitrary rule, it is a direct requirement of energy conservation. Suppose, for a moment, that the current flowed the OTHER way, attracting an approaching magnet instead of repelling it: the magnet would then accelerate toward the coil faster and faster, gaining kinetic energy from nothing, a perpetual motion machine, plainly impossible. The correct direction, a repelling force resisting the push, means a person moving the magnet must do real mechanical work against that resistance, and it is precisely this work that gets converted into the electrical energy of the induced current, which is itself eventually dissipated as heat. Lenz's law, in other words, is simply energy conservation, applied to electromagnetic induction, and the negative sign in ε = -dΦB/dt is its exact mathematical expression.

A conductor sliding through a magnetic field, rather than a fixed coil sitting in a changing one, offers a second, equally valid route to the exact same physics. Picture a rod PQ, free to slide along two parallel rails RS forming a closed rectangle, sitting in a uniform field B perpendicular to the whole arrangement; as the rod moves left with speed v, the loop's enclosed area shrinks, changing the flux, ΦB = Blx, where x is the rod's shrinking distance from the fixed end. Applying Faraday's law directly, ε = -dΦB/dt = -Bl(dx/dt) = Blv, a clean, purely geometric result called motional emf. The very same result also follows from a completely different starting point: the Lorentz force. Every free charge inside the moving rod is itself travelling at speed v through the field B, so each one feels a genuine sideways force of magnitude qvB, pushing positive charge toward one end of the rod and leaving the other end relatively negative; the work done moving a charge q the rod's full length l is W = qvBl, and since emf is defined as work done per unit charge, ε = W/q = Blv, exactly matching the flux-based calculation. These two derivations describe the same physical situation from two different vantage points, yet a subtlety lurks underneath: when the CONDUCTOR moves through a static field, the Lorentz force q(v x B) genuinely does the work; but when instead the conductor sits still and the FIELD itself changes with time, there is no v x B force at all (since v=0), and yet an emf is induced just the same. The only way to make sense of this second case is to accept that a time-varying magnetic field itself generates an electric field, an idea with no counterpart at all in the electric fields produced by static charges, and the deep, symmetric heart of what Faraday actually discovered.

A changing current in one coil can induce an emf in a neighbouring coil, and, remarkably, a changing current can even induce an emf back in the very SAME coil it flows through. Both effects share one underlying fact: flux is always proportional to current, ΦB proportional to I, for a coil whose geometry stays fixed, so the RATE of change of flux is proportional to the RATE of change of current too. For a closely-wound coil of N turns, the total flux linkage, NΦB, threading through every turn, is what actually matters, and the constant of proportionality between this flux linkage and the current producing it is called inductance, NΦB = (constant) x I. Inductance depends only on a circuit's geometry, its shape, size, number of turns, and on the intrinsic magnetic properties (the permeability) of whatever medium fills it, genuinely never on the current or flux themselves at any given instant, in exact analogy with how a capacitor's capacitance depends only on its plates' geometry and the dielectric between them, never on its instantaneous charge or voltage. Inductance is a scalar quantity, measured in henry (H), named for Joseph Henry, and its SI dimensional formula works out to flux divided by current. Two distinct but closely related situations fall under this single idea: mutual inductance, where a changing current in one coil induces an emf in a separate, nearby coil, and self-inductance, where a coil's own changing current induces an emf back within itself.

Consider two long, coaxial solenoids sharing the same length l, one inside the other; the inner solenoid S1 has n1 turns per unit length and radius r1, the outer S2 has n2 turns per unit length and radius r2. Send a current I2 through the outer solenoid S2, and it produces a field m0n2I2 inside itself, threading through the inner solenoid S1 as well; the resulting flux linkage with S1 works out to N1F1 = m0n1n2pr1²l x I2, so the mutual inductance of S1 with respect to S2 is M12 = m0n1n2pr1²l. Now reverse the roles: send a current I1 through the INNER solenoid S1 instead. Since S1's own field is confined essentially entirely within its own smaller radius, the flux linkage induced in the outer coil S2 works out, after a similar calculation, to exactly the SAME expression: M21 = m0n1n2pr1²l. Despite arising from two apparently quite different calculations, one where the source solenoid's field is easy to treat as uniform across the other's whole cross-section, the other where it very much is not, M12 and M21 always come out equal, M12 = M21 = M, a genuinely deep and remarkably useful general result, true far beyond this one coaxial-solenoid example. Its practical value is considerable: whenever calculating the mutual inductance one way around is difficult (the source coil's field varying awkwardly across the other's area), calculating it the OTHER way around, if easier, gives the exact same answer. A changing current I2 in the second coil then induces an emf in the first, e1 = -M dI2/dt, the size of the induced emf set jointly by how fast the current changes and by the two coils' mutual inductance, itself fixed by their shared geometry, separation and relative orientation.

It is equally possible for a coil to induce an emf entirely within itself, with no second coil involved at all: as a coil's OWN current changes, its OWN flux changes too, and this self-induced change generates an emf right back in that same coil. The flux linkage of an N-turn coil is proportional to its own current, NFB = LI, where L, the self-inductance, plays exactly the same defining role as mutual inductance did before, just for a single coil acting on itself. Differentiating gives the self-induced emf directly, e = -L dI/dt: crucially, this emf always opposes ANY change in the coil's own current, whether the current is increasing or decreasing, which is precisely why it is also called the back emf. For a long solenoid of cross-sectional area A, length l, and n turns per unit length, carrying current I, the field inside is B = m0nI, and the total flux linkage works out to NFB = m0n²Al x I, giving a self-inductance of L = m0n²Al, depending only on the solenoid's own geometry, not on the current flowing through it at any instant; filling the solenoid's core with a material of relative permeability mr scales this up directly, L = mrm0n²Al. Physically, self-inductance behaves exactly like inertia in mechanics: mass resists a change in velocity, and self-inductance resists a change in current, in both cases regardless of which direction the change is happening in. Establishing a current against this resistance genuinely requires work, work that does not vanish, but gets stored as magnetic potential energy in the inductor's own field, ready to be released again the moment the current is allowed to fall.

Pushing current through an inductor against its own back emf costs real work, and tracking that work gives a genuinely satisfying result. At any instant, power delivered against the back emf is dW/dt = eI, and using e = L dI/dt (ignoring its sign here, since work is being done against it), this becomes dW/dt = LI dI/dt; integrating from zero current up to a final current I gives the total energy required, W = the integral of LI dI from 0 to I, which works out to W = (1/2)LI², a result that echoes (1/2)mv², the kinetic energy of a mass m moving at speed v, precisely because L plays the same inertial role for current that mass plays for velocity. This energy is not lost, it is genuinely stored in the inductor's own magnetic field, recoverable again as the current is allowed to fall. For a solenoid specifically, substituting L = m0n²Al and B = m0nI lets this energy be rewritten entirely in terms of the field itself, W = B²Al/2m0; dividing by the volume Al enclosed by the field gives an energy density, uB = B²/2m0, the magnetic field's own stored energy per unit volume. This expression, though derived here for the special case of a solenoid, turns out to hold generally, for a magnetic field of any origin whatsoever, and it bears a striking resemblance to the electric field's own energy density, uE = (1/2)e0E², encountered earlier when studying capacitors: both energies scale with the square of the field strength, a shared mathematical shape that is no coincidence, and a first hint of just how closely related electric and magnetic fields ultimately turn out to be.

Rotating a coil steadily inside a uniform magnetic field is a genuinely practical way to keep changing its flux continuously, without ever needing to move a magnet back and forth, and is exactly the working principle behind the AC generator. A coil, called the armature, is mounted on a shaft and mechanically rotated, by falling water in a hydroelectric plant, by steam in a thermal or nuclear plant, or by any other suitable mechanical source, inside a fixed magnetic field B; its ends connect to the external circuit through sliding contacts called slip rings and brushes. As the coil turns at a constant angular speed w, the angle between the field and the coil's own area vector at any time t is simply q = wt, so the flux through it varies smoothly, FB = BA cos wt. Applying Faraday's law directly to this steadily changing flux gives the instantaneous induced emf for a coil of N turns: e = NBAw sin wt, or, writing e0 = NBAw for the maximum value the emf ever reaches, e = e0 sin wt. Since the sine function swings smoothly and continuously between +1 and -1, the induced emf's own polarity reverses periodically too, exactly what makes the resulting current an ALTERNATING current, reversing direction at a steady, predictable rate rather than flowing in one direction only. The emf peaks whenever the coil's plane lies exactly along the field (q = 90 degrees or 270 degrees), the instant the flux is changing fastest, and drops to zero whenever the coil's plane is exactly perpendicular to the field, the instant the flux briefly stops changing at all. Modern generators can produce hundreds of megawatts this way; in most large power stations, it is actually more practical to keep the coils fixed and rotate the electromagnets producing the field instead, though the underlying physics is identical either way, and Indian power grids run this cycle at 50 hertz, fifty complete reversals every second.