Self Inductance Consider a solenoid with n turns/m, length l, current i, and cross sectional area A. l A There is a magnetic field inside the solenoid, parallel to its axis with value: This field creates a flux through the same device (the solenoid) that creates the field. Should the field change (maybe change the current), the flux will change and there will be an induced voltage and current. This process is called self induction.

What is the total flux,  B,through the solenoid? measured in Henrys If the current changes, then Faraday’s law gives: If L is not easily calculable from 1 st principles, we can measure it using the above equation: Both quantities on rhs are easy to measure

The circuit symbol for an inductor is: When the current is changing in the inductor, there will be a voltage drop across it: Compare this with the other circuit devices you have studied: battery resistor capacitor

RL Circuit R Є L At t = 0 we close the switch up to put battery in series with L and R. What does Kirchhoff say? i

Energy in Inductors and Magnetic Fields Let’s take the loop equation for the building inductor circuit and multiply by the current: Power supplied by battery Power consumed by resistor Power consumed by inductor Thus

For a solenoid: Dividing by the volume Al, we get the energy density in the magnetic field:

Exercise; Suppose a large inductor of 10 H is effectively connected in series with a small resistance of of 1Ω. A knife-blade switch is used to turn the circuit on and off, and eventually a current of 10 A is established in the inductor. Why might the person turning the circuit off want to have a lot of insurance? The energy stored in the inductor is: As the switch is opened quickly, a huge voltage will develop. Why? Large di/dt This energy will be discharged in about: