6.5 Generators, Lenz’s Law, and Faraday’s Law

In a solenoid, current in a wire effectively moves round in coils to produce a magnetic field, and in a motor, current in a field produces motion. Now we will discuss the third option, field and motion.

When a wire, connected to a sensitive ammeter (from Ampère-meter - a device that measures current), is moved through a magnetic field, an E.M.F. is induced. Since the wire is part of a closed circuit, providing a path of conduction, a current will flow in the wire (which is detected by the ammeter). However, the current only flows as long as the wire is moving in the field; once it has left it, it ceases to flow. Also, a slower-moving wire in a field produces less current. To find the direction of the current induced, you only need your hand, but this time, it is the right hand.

Once again, the thumb stands for the motion of the wire, the first finger points in the direction of the field, and the second finger will tell you which way the current will flow in the wire. Remember to hold the three fingers so they are all at right angles with each other. This rule is Fleming’s Right Hand Rule.

In this diagram, the red wire (in a properly closed circuit, of course) is moved up through the field. By using the Right Hand Rule, we find that the current induced in the wire flows towards the back of the picture. But wait! What happens when the Left Hand Rule is used, now that we know the direction of the current? We find that when the current flowing in the wire exists in the magnetic field that induced it, the new motion of the wire would be opposite to the motion it was actually moved!. Thus, the current produced is in a direction that actually opposes the change (this case, the motion) producing it. This is Lenz’s Law.

Let’s just say, for a moment, that the opposite was true. By moving a wire through a field, a current would be produced. This current, being in a field, would continue moving the wire through the field (instead of trying to move it in the opposite direction). This, in turn, would produce a current . . . In short, what would have been created is a self-perpetuating system that continues increasing in both motion and current, both of which require a lot of energy. This is where our theory fails. We forget a one of the most important laws of physics, the law of conservation of energy. What we would be doing is creating infinite energy from nothing but merely inching a wire through a field. Since energy cannot be created nor destroyed, this entire situation is impossible.

Lenz’s Law helps to explain what happens when a magnet is passed through a solenoid. As the magnet is pushed into the solenoid, the current induced in it creates an electromagnet out of the solenoid; an electromagnet that repels the magnet inside of it already. This means you have to do work against the repulsive force in order to get the magnet through. However, once the magnet leaves the solenoid, you might expect that the repulsive force would continue. Unfortunately, this is not the case. When the magnet has left the solenoid, the current induced in the coils is such that an attracting electromagnet is created. This means that work has to be done against an attractive force, in order to move the magnet away from the solenoid.

Now onto electromagnetic induction. Take the simplified motor that was discussed in the previous section. However, instead of connecting the carbon brush contacts to a power source, let us connect it to something that uses energy instead, a resistor in the form of a light bulb.

As we turn the handle in the picture, the wire loop rotates (note: this is in the opposite direction as the last use). This moves the wires through a field. Because of the split-ring commutator, the side of the loop on the left always produces current flowing out of the loop, and the side on the right always has current flowing in. This means that a D.C. current is produced. A.C. current can also be produced, using two slip rings instead of the split ring commutator. Each side of the wire loop is connected to a separate ring, which is in turn connected to a brush contact. As a side of the loop rotates, it moves first in one direction through the field, than in the opposite. This produces an A.C. output at each ring, and therefore for the entire circuit.

An E.M.F. (voltage), as well as a current, is produced by this simple generator, in a process called electromagnetic induction. This voltage, also called an induced E.M.F., is then used in the circuit to light the light bulb. The voltage is produced because there is mechanical power going into the handle of the generator. Power yields both current and voltage, as you may recall from Unit 6.1

Faraday’s Law better describes this: an E.M.F. is induced in a conductor (i.e. a coil) when the magnetic field around it changes. The magnitude of the E.M.F. is proportional to the rate of change of the field, or rate of cutting flux, while its direction depends on the direction of the rate of change.

The constant of proportionality is equal to N, the number of turns in the coil cutting the flux, so :

Note: the negative sign indicates that the E.M.F. opposes the change producing it.

The term N df is called flux linkage, and is given by the product of the number of coils and the field lines.