Page:Elementary Text-book of Physics (Anthony, 1897).djvu/381

§ 307] in these experiments is, easily seen to be in accordance with the law above stated. A simple statement, known as Lenz's law, which enables us to determine the sense of an induced current produced by the motion of a magnet or a circuit, is as follows: When an induced current is produced, it is always in such a sense as to oppose the action which produces it. This is equivalent to the statement that the induced current tends to oppose the change in the number of tubes of induction which pass through the circuit.

The case in which an induced current in the secondary circuit is set up by making the primary circuit is, as has been said, an extreme case of the movement of the primary circuit from an infinite distance into the presence of the secondary. The experiments of Faraday and others show that the total quantity of electricity induced when the primary circuit is made is exactly equal and opposite to that induced when the primary circuit is broken. They also show that the electromotive force induced in the secondary circuit is independent of the materials constituting either circuit, and is proportional to the current strength in the primary circuit. These results are consistent with the formula already deduced for the induced current.

307. Currents of Self-induction.—If the current in a circuit be changed, the number of tubes of induction which pass through the circuit will vary, and an induced current will be set up in the circuit. If there be originally no current in the circuit and if an electromotive force be suddenly impressed upon it, so that the current which finally exists in the circuit is $$i,$$ the number of tubes of induction developed through the circuit as equal to $$Li$$ (§ 293). Let $$t$$ be the time required for the current to rise to its full value; then the average electromotive force induced in the circuit by the increase in the number of tubes of induction which pass through it will be $$\frac{Li}{t},$$ and the average current will be $$\frac{Li}{rt}\cdot$$ The total current due to this induced electromotive force is therefore $$\frac{Li}{r}$$ and is opposed, in sense, to the current impi-essed upon the circuit. If the circuit be suddenly broken, the same expression represents the total