chapter28

Magnetic Flux
Magnetic flux woks just like electric flux except with magnetic fields. Simply put, it's the number of magnetic field lines that penetrate a surface.



The unit for magnetic field is the **weber** (Wb) equal to one tesla meter squared.



When the surface is flat, as with a loop, and the magnetic field is constant the equation becomes simple!

Induced EMF and Faraday's Law
Experiments by Faraday, Henry and others have shown that if the magnetic flux through a surface bounded by a circuit cause an EMF (Electromotive Force or voltage) in the circuit equal to the rate of change in the flux.

In equation form we can write: This is **Faraday's Law** Magnetic flux in a circuit can be changed several ways:
 * Current producing magnetic field could be changed
 * Permanent magnet can be moved towards or away from the circuit
 * The circuit could be rotated in a magnetic field
 * The area of the circuit could be changed

In all of these cases, the changing magnetic flux would cause an induced emf in the circuit due to Faraday's Law

Lenz's Law
the change that produced it. Put another way, when the magnetic flux through a surface changes, it produces a magnetic flux of it's own in the other direction. Above, the north side is going towards the loop. By Lenz's law, the magnetic field due to the induced current in the loop is the opposite way. We can then find the direction of the current using the second right hand rule.
 * Lenz's law** explains the negative sign in Faraday's Law. Lenz's law says that the induced emf is in such a direction to oppose

[[image:figure-28-13.jpg width="400" height="173"]]
If the loop is moving away from the magnet, the change is the opposite way, so the induced current goes in the opposite direction, causing a magnetic field to oppose the change. If in the above examples the magnet were flipped then the current would be flipped.

If we begin to think about it, Lenz's Law makes a lot of sense. If, for instance, the created amgnetic field was the other way, then if we were to put a magnet in a coil of wire, it would create a current and be pulled farther into the coil. This would therefore add energy to the system violating conservation of energy. For this reason, it makes a lot of sense that Lenz's Law should apply in the direction specified.

Motional EMF
Motional emf is any emf induced by the motion if a conductor in a magnetic field. For instance, if we have a rotating loop of wire, the angle with the magnetic field is changing so the flux is changing which induces an emf by Faraday's Law.

The genral equation for motional emf is However, most of the time the problems are much simpler and can easily solved by finding the change in th flux and deducing the emf from that.

Inductance
If we were to put a coil of wire in a circuit, the magnetic flux throught it would be proportional ot the current in the wire. L is the self--inductance of the coil which depends on the shape of the coil. The units for self-inductance are the **henry** (H). Calculating the inductance of a long tightly wound coil can be done quickly and effectively.  where n is the number of turns per unit length and l is the length.

This coil of wire is called an inductor. When we put an inductor in a circuit, it will do nothing when the current is constant. However, when the current changes in the circuit, the change will change the magnetic field and flux inside the inductor. As a result, by Faraday's Law, the inductor will create a back-emf which resists the change in the current in the circuit. The phenomenon is known as **self-induction**. The magnitude of the back-emf is

Magnetic Energy
Inductors store magnetic energy in a circuit, just like capacitors store electric energy. The energy comes from the magnetic field within the inductor that occurs when current os passed through it. Through equation manipulation, we can get the equation for the energy stored in an inductor. The equation for potential energy in an inductor is   If we have a charged capacitor and an inductor in a series, this equation can be used in combination with the equation for energy stored in a capacitor and conservation of energy to obtain current and charge stored on the capacitor.

RL Circuits
Circuits that contain an inductor and a resistor are RL circuits.  If we series them in a loop with a battery, we get the following equation for Kirchnoff's loop rule.  This differential equation when solved gives us the following equation for current   where t is time since switch is switched on. So, after a while, the current approaches the current that would exist if there was no inductor.

Lab
Lab Procedure and Questions: Answers:

[[file:Lab-EM2[answers].doc]]


Thanks to Tipler and Mosca's //Physics for Scientists and Engineers// for images and resources.


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