Inductance

 According to the Faraday's law, a changing (time-dependent) magnetic field B will induce an electric field, known as the electromotive force (emf) field. If the magnetic field is transverse to a single-loop coil, the emf field will generate an emf voltage V across the two ends of the coil:

(Equation 1)

The magnetic flux through the loop is,

where A is the area of the loop, and if the magnetic field B is along a general direction, B must be replaced with its component perpendicular to the area of the loop, and ΔΦ/Δt is the rate of its change. The minus sign in Equation 1 signifies the direction of the induced emf (or voltage): it always tries to oppose the change of the external B field by generating a current in the coil that produces its own magnetic field in the opposite direction of the change of the B field. The direction of the induced magnetic field is related to the direction of the current in the coil by the red hand rule (wrap the fingers of the right hand around the current direction, the thumb points in the direction of the magnetic field produced by the current). For example, if the external B field is along the +x direction (the area of the loop is in yz plane) and is increasing with time, then the magnetic field generated by the induced emf and current will be in the -x direction; if the external B field is decreasing, the induced emf and current will generate a magnetic field in the +x direction. This is the phenomenon of magnetic induction. For a "solenoid" coil of N turns, the emf voltage generated by each turn will add up to a total emf voltage. During the magnetic induction, the coil can be thought of as an analogue of a battery that would output a voltage and (if some load is connected) a current. In this experiment, this phenomenon will be demonstrated using an increasing or decreasing magnetic field B produced by: (1) a permanent magnet moved toward or away from the coil (Figure 1); (2) another coil with a current I flowing through the coil, where I can be switched on or off (Figure 2); and (3) the coil itself with a current I flowing through, where I can be switched on or off (Figure 3). In the case of (3), the induction is referred as self-induction (and the solenoid is an example of an "inductor"). For both cases (2) and (3), since the magnetic flux or magnetic field (whose change causes the induction) is proportional to the current I, the induced emf voltage is proportional to the rate of the change of the current (ΔI/Δt), with the proportional factor L known as the mutual inductance as in case (2) or self-inductance as in case (3), respectively:

(Equation 2)

The direction of the voltage V is determined in a similar manner as described above: the emf V will try to produce a current I, and its own magnetic field that opposes the change in the original magnetic field B.

Representative results for what may be observed on the ammeter reading for Sections 1 and 2 (setups in Figures 1 and 2) are summarized in Tables 1 and 2 below.

Table 1: Representative results for Section 1. For step 1.8, observe that a faster speed of motion gives a larger reading (larger needle deflection) on the ammeter.

Table 2: Representative results for Section 2. For step 2.6, observe that placing coil #2 inside coil #1 gives a larger reading (while the signs of the reading remain the same) on the ammeter compared to step 2.5 for each corresponding switch action.

For Section 3, if initially the current due to the volt supply (+1 V) is flowing from the right to the left in the coil, turning it off (opening the switch) will induce a transient current along the same direction. The light bulb will light up briefly, and the ammeter will register a positive reading for the connection given in Figure 3.

In this experiment, we have demonstrated how changing a magnetic field (by moving a magnet) induces a current in a coil, and also how changing the current in the coil induces current in another coil (mutual induction). We also demonstrated that changing the current in a coil induces a voltage and current in the same coil (self-induction).

Inductors (typically in the form of coils) are commonly used in many circuit applications, such as to store magnetic energy when a steady state current flows. They are useful for electrical signal processing; for example, taking the derivative or integral of an electrical signal, for filtering, and for resonance circuits. They are also used in transformers to change the voltage of AC signals.

The author of the experiment acknowledges the assistance of Gary Hudson for material preparation and Chuanhsun Li for demonstrating the steps in the video.