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Inductance

# Inductance

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Inductors -- typically in the form of coils -- are commonly used in many circuit applications. Their purpose is to store magnetic energy when a steady state current flows.

In a loop that forms a closed circuit, the changing magnetic field induces an electromotive force that drives the current. This phenomenon is called electromagnetic induction. An inductor is simply a coil of wire and it has the property of self-inductance, which relates the voltage across its terminals with the change in its own magnetic field.

This video will illustrate the concepts behind inductance and then demonstrate an induction experiment using a bar magnet and a coil. Lastly, we will review some of the current applications for inductors.

Magnetic flux may be thought of as the amount of magnetic field passing through an area. For a uniform magnetic field B perpendicular to an area A, magnetic flux phi is simply the product of the two. According to Faraday's law of induction, a changing magnetic flux in a loop of wire generates an electromotive force, or EMF, along the loop. This EMF is equal to the negative of the rate of change of magnetic flux over time.

The magnetic flux's rate of change determines the polarity of the induced electromotive force. The negative sign in the expression for Faraday's law means that if the magnetic field decreases with time, the EMF is positive. If it increases with time, the EMF is negative. When the loop is a closed circuit, the induced EMF drives current that in turn generates its own magnetic field. This magnetic field has an orientation given by the Right Hand Rule. If the fingers of the right hand curl around the direction of current in the loop, then the thumb of the right hand would point in the direction of the generated magnetic field. The induced current must flow in the direction that creates a magnetic field opposing the external magnetic field's rate of change.

For example, the magnetic field from this magnet points upward through a single loop of wire. Moving the magnet away from the loop decreases the magnetic field strength through the loop. The change in magnetic flux- represented by a vector pointing downward-induces a positive EMF that drives current counterclockwise as shown. By the Right Hand Rule, the current creates a magnetic field that points up within the loop to oppose the decreasing magnetic field or flux. In contrast, moving the magnet toward the loop increases the magnetic field there. The change in magnetic flux is represented by a vector pointing upward. In this case it induces a negative EMF that drives current clockwise. By the Right Hand Rule, current in this direction creates a magnetic field that points down within the loop to oppose the increasing magnetic field or flux.

Now let's move on from a loop to a solenoid, which is simply multiple loops of wire wound around a core of air or magnetic material. It is a commonly used inductor in electrical circuits. If current flows through a solenoid, it creates a magnetic field within the inductor. The direction of this magnetic field is given by the right hand rule. This field in turn produces a magnetic flux in the direction same as that of the field, and the amount of this flux is proportional to the current. Therefore, if the current changes with time, so does the magnetic flux. Following the Faraday's law, the changing flux induces a voltage that drives current through the coil such that the induced current's magnetic field opposes the change in the original flux. This phenomenon of voltage induction across its own terminals in response to varying current is called self-induction, and the total induced voltage across the solenoid is the number of turns N, multiplied by the EMF of a single loop.

Now that we've explained the basics, let's see how to study electromagnetic induction in a physics lab.

All of the following experiments use an analog bipolar ammeter, which has a needle that deflects to the right or left of the zero point, depending on the direction of current flow.

First, obtain a solenoid with a hollow core, a rod magnet with clearly labeled north and south poles, and the analog bipolar ammeter. Then connect the solenoid to the ammeter. For the first trial, insert the north pole of the magnet into the end of the solenoid connected to the negative terminal of the ammeter. Observe the ammeter and record the polarity and approximate magnitude of the needle's deflection. Pull the magnet out of the solenoid and record the polarity and approximate magnitude of the ammeter needle's deflection.

Now turn the magnet around and insert and remove the south pole from the end of the solenoid connected to the negative terminal of the ammeter. Repeat this experiment by inserting the south pole of the magnet into the coil and then removing it-first more slowly and then more quickly than in the first trial. When the north pole moves near and enters the solenoid, it induces current that causes a momentary positive deflection of the ammeter. When the north pole is removed from the solenoid, the deflection is negative. Reversing the orientation of the magnet also reverses the ammeter response.

Finally, the speed of movement affects the change of magnetic field with time, which determines the induced voltage and current. Slower motion induces less current and a smaller reading, and faster motion induces more current and a larger reading.

For the self-inductance experiment, connect a light bulb, inductor coil, voltage supply set at positive one volt, switch, and the analog ammeter as shown. Assemble the circuit with the switch open so no current flows.

Close the switch to connect the voltage source to both the light bulb and inductor coil. Observe the bulb, which appears to be dimly lit. Open the switch to disconnect the voltage supply from the circuit. Observe the light bulb and the ammeter at the moment the switch is opened then record the result. The light bulb brightens briefly and the ammeter shows a positive reading at the same time. This happens due to self-induction and several events take place during this brief period of time.

Initially, when the switch is closed, current flow through both the coil and light bulb, but much more current flows through the coil compared to the light bulb, since the coil has lower resistance compared to the bulb. Opening the switch disconnects the voltage source. This causes the current through the inductor to decrease.

This changing current through the inductor causes a change in its magnetic flux, which in turn induces a transient current that opposes the decrease by flowing in the same direction as the original current. The combination of the two - original and transient current -- yields the total inductor current, which now flows through the bulb and lights it up briefly, and at the same time causes a deflection in the ammeter to indicate a positive current.

Electromagnetic induction has many applications in modern devices, and is a fundamental method of transferring energy and information without physical contact.

Induction is the core principle behind the functioning of devices called transformers. A transformer has a pair of input terminals connected to a primary winding-or coil-and a pair of output terminals connected to a secondary winding. A core consisting of steel, ferrite or even simply air, magnetically couples the two windings. A voltage across one winding causes current to flow through it, creating a magnetic field. Magnetic flux, or the density of the magnetic field, is then coupled to the secondary winding through the core, where it induces a voltage. This principle is called mutual induction.

Another application of inductors is AC induction motors, which are the workhorses of modern industry due to their simplicity, ruggedness, and reliability. An induction motor has only two main parts. The first is the stationary part, called the stator, which consists of stationary coils around a cavity. Suspended in the cavity is the rotor, which is a pair of end rings capping a cylindrical arrangement of bars. A three-phase AC induction motor uses three-phase power, with each phase connected to its own, separate set of stator coils. The coils are arranged in a pattern that generates one magnetic field for each phase of the supplied power. The resulting net magnetic field, called the "stator magnetic field" rotates with constant velocity.

The rotating magnetic flux induces current in the rotor, similar to the way that a transformer transfers power from the primary coil to the secondary. The current through the bars of the rotor in turn creates its own magnetic field, called the "induced rotor magnetic field." The interaction between these two fields produces a force on the rotor, which causes it to follow the stator magnetic field, like an iron bar following the magnets around it.

You've just watched JoVE's introduction to electromagnetic inductance. You should now understand how a time varying magnetic field induces an electromotive force in a conductor, and how the resulting current produces its own magnetic field. Thanks for watching! X 