As we know, any magnetic field that changes over time will create an electric field. The induced electric field is perpendicular to the magnetic field, and forms a curly pattern around it. Any electric field that changes over time will create a magnetic field.
The induced magnetic field is perpendicular to the electric field, and forms a curly pattern around it. The electric company uses a device called a transformer, to convert everything to lower voltages and higher currents inside your house. The coil on the input side creates a magnetic field. Transformers work with alternating current (currents that reverses its direction many times a second), so the magnetic field surrounding the input coil is always changing. This induces an electric field, which drives a current around the output coil.
Since the electric field is curly, an electron can keep gaining more and more energy by circling through it again and again. Thus the output voltage can be controlled by changing the number of turns of wire on the output side.
In any case, conservation of energy guarantees that the amount of power on the output side must equal the amount put in originally:
(input current) × (input voltage) = (output current) × (output voltage)
So no matter what factor the voltage is reduced by, the current is increased by the same factor. This is analogous to a lever. A crowbar allows you to lift a heavy boulder, but to move the boulder a centimeter, you may have to move your end of the lever a meter. The advantage in force comes with a disadvantage in distance. It’s as though you were allowed to lift a small weight through a large height rather than a large weight through a small height. Either way, the energy you expend is the same.
Somewhere on your street is a transformer, one side of which is connected to the lamp’s circuit. When the lamp is plugged in and turned on, there’s a complete circuit, and current flows. as current flows through the coils in the transformer, a magnetic field is formed — remember, any time there’s moving charge, there will be magnetic fields. Because there is a large number turns in the coils, these fields are fairly strong, and store quite a bit of energy.
When you pull the plug, the circuit is no longer complete, and the current stops. Once the current has disappeared, there’s no more magnetic field, which means that some energy has disappeared. Conservation of energy tells us that if a certain amount of energy disappears, 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 magnetic fields. One is the principle of induction, and the other is the idea that according to relativity, observers in different frames of reference must perceive different mixtures of magnetic and electric fields. At the time Faraday was working, relativity was still 70 years in the future, so the relativistic concepts weren’t available — to him, his observations were just surprising empirical facts. But in fact, the relativistic idea about frames of reference has a logical connection to the idea of induction.
Assume: Observer A is at rest with respect to the bar magnets, and sees the particle swerving off in the z direction, as it should according to the right-hand rule. Suppose observer B, on the other hand, is moving to the right along the x axis, initially at the same speed as the particle. B sees the bar magnets moving to the left and the particle initially at rest but then accelerating along the z axis in a straight line. It is not possible for a magnetic field to start a particle moving if it is initially at rest, since magnetism is an interaction of moving charges with moving charges. B is thus led to the inescapable conclusion that there is an electric field in this region of space, which points along the z axis. In other words, what A perceives as a pure magnetic field, B sees as a mixture of electric and magnetic fields. This is what we expect based on the relativistic arguments, but it’s also what’s required by the principle of induction. In B’s frame of reference, there’s initially no magnetic field, but then a couple of bar magnets come barging in and create one. This is a change in the magnetic field, so the principle of induction predicts that there must be an electric field as well.