6.4. FARADAY'S LAW OF INDUCTION

From the experimental observations, Faraday arrived at a conclusion that an emf is induced in a coil when magnetic flux through the coil changes with time. Experimental observations discussed in Section 6.2 can be explained using this concept. The motion of a magnet towards or away from coil C in Experiment 6.1 and moving a current-carrying coil C towards or away from coil C in Experiment 6.2, change the magnetic flux associated with coil C. The change in magnetic flux induces emf in coil C.

Faraday's Law states that an electromotive force (emf) is induced in a coil of wire whenever there is a change in the magnetic flux through that coil over time. This is fundamental to understanding how electrical power is generated. For instance, if you move a magnet towards or away from a coil, the magnetic field around the coil changes, leading to a change in magnetic flux. This change induces an emf in the coil, causing current to flow if the circuit is closed.

Think of this process like water flowing through a hose. If you squeeze the hose (representing changing the magnetic field), the water (electric current) flows differently. Just as a squeeze in the hose causes an immediate response in water flow, altering the magnetic field relative to the coil causes an immediate response in the induced current.

A plausible explanation for the observations of Experiment 6.3 is as follows: When the tapping key K is pressed, the current in coil C (and the resulting magnetic field) rises from zero to a maximum value in a short time. Consequently, the magnetic flux through the neighbouring coil C also increases. It is the change in magnetic flux through coil C that produces an induced emf in coil C. When the key is held pressed, current in coil C is constant...

In Experiment 6.3, pressing the key leads to a sudden increase in current in a coil, which creates a magnetic field. This change in the magnetic field causes the magnetic flux through a nearby coil to change. The varying magnetic flux induces an emf in the neighboring coil because it is coupled through the changing magnetic field. Importantly, once the key is pressed and the current stabilizes, the induced emf disappears since there are no longer changes in flux. Finally, releasing the key rapidly decreases the current, which again changes the magnetic flux, inducing an emf in the opposite direction.

Imagine a photographer adjusting a dimmer switch to increase light in a room. As they gradually increase the light, people in the room start to notice the brightness (analogous to increasing current), but once the light stays at a constant level, no one notices further changes until the switch is lowered back down. The initial adjustment increases light slowly, causing gradual changes in brightness.

1.6 The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit. Mathematically, the induced emf is given by e = -dF/dt. The negative sign indicates the direction of e and hence the direction of current in a closed loop.

The mathematical representation of Faraday's Law captures the relationship between the change in magnetic flux and the induced electromotive force (emf). The formula e = -dF/dt indicates that the induced emf is directly related to how fast the magnetic flux changes through the loop. The negative sign, a significant element of Lenz's law, tells us that the induced current will flow in a direction that opposes the change in magnetic flux, preserving energy in the system.

Consider a person pulling a water bucket from a well. If they pull it faster (analogous to a rapid change in magnetic flux), more effort is required to keep the bucket moving, and the same principle applies to changes in magnetic flux and the resulting current: the quicker the change, the larger the current induced. The opposing current can be likened to the resistance felt in the well's bucket due to water pressure.

In the case of a closely wound coil of N turns, change of flux associated with each turn is the same. Therefore, the expression for the total induced emf is given by e = -N(dF/dt).

When dealing with coils that consist of multiple turns (N turns), Faraday’s Law must account for each individual turn experiencing the same change in magnetic flux. Thus, the total emf induced in the coil is the sum of all the individual contributions for each turn, leading to the expression e = -N(dF/dt). It emphasizes the cumulative effect of multiple loops of wire encountering changes in the magnetic environment.

Think of a group of people holding onto a rope. If one person tugs the rope quickly (indicating a change in magnetic flux), all others feel that tug due to the rope being pulled, similar to how each loop in the coil responds to the changing magnetic field together to create a stronger total response.

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