An Introduction to the Mathematical Theory of Electricity And Magnetism

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Then we have Thus the work done to keep t\ steady in A against the induc- tive action of B is 11. If a given circuit is carrying a varying current it is pro- ducing a varying quantity of magnetic induction through itself. Thus there must be an induced E. M. F. In the circuit in conse- quence of the variation of the current that it carries. Now the quantity of induction through the circuit due to its current is generally proportional to its current. For unit current in the circuit let this quant...ity be L. L is called the coefficient of self- induction of the circuit : and we have for its definition, DEF. : THE COEFFICIENT OF SELF-INDUCTION of a circuit is the quantity of induction passing through it per unit current in it.
L will depend on the form and size of the circuit, and on the magnetic susceptibilities of any neighbouring substances. Sup- pose we know the value of L for a circuit of a single turn, and have a circuit of n turns all occupying practically the same position as the single turn, then the value of L for this circuit will be obtained by multiplying that for a single turn by n 2, for we have now produced the same effect as if we had made the M 1 62 Electro- Magnetic Induction.


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