Electromagnetism Faraday & Maxwell

Faraday Michael Faraday (1791 – 1867) was an English scientist. He was a genius at experimental design and conceptualization (and an incompetent mathematician).

Observations Holding a magnet in front of a coil of wires does not induce a current. Pushing the north pole of a magnet through the coil induces a current in one direction. Pulling the north pole of a magnet back out of the coil induces a current in the other direction. The bigger the area of the coil, the larger the current. Twisting a magnet in front of a coil of wires causes a current only while the magnet is moving. Rutgers: exampleexample

Induction A changing magnetic field around a coil of wires induces a potential difference, . Investigate this simulation.this simulation

Induction A changing magnetic environment around a coil of wires induces a potential difference, .  Strength of magnet   voltage  Area of coil   voltage  Number of coils   voltage  Rate of change of magnetic field   voltage

Flux In physics, when we talk about “flux”, we refer to the number of things passing through or hitting a certain area. Number of tennis balls landing in a particular area on the tennis court Number of photons hitting your retina Number of magnetic field lines passing through a particular area.

Flux For purposes of electromagnetism, magnetic flux refers to the strength of magnetic field times the area: 1 tesla  1 square meter = 1 weber 1 W = 1 T  1 m 2 We use the Greek letter phi (pronounced ‘fee’ or ‘fie’) subscript B to denote magnetic flux,  B Wilhelm Weber, German, 1804 – 1891: investigated electricity and magnetism, co-invented telegraph. More herehere

Changing flux: 1)With magnets of different strength  B results in denser field lines and    B

Changing flux: 2) With different sizes of coils  A results in more field lines and    B

Changing flux: 3)At different angles   results in more field lines and    B

At different angles (cont’d)  B  B  where B  = component of magnetic field perpendicular to coil = B (cos  )  B  B (cos  )

Changing flux: summary

How do we change induced current? This relationship is called Faraday’s Law (but was articulated by James Maxwell)

Example Try it first

Example Try it first

Example Suppose you rotate a square coil of wires with side length 5.0 cm in a magnetic field of strength 0.16 T. If it takes the coil 0.14 s to go from being perpendicular to the field to 30 , how much current flows? Assume a resistor of . Try it first

“Motional” 

Example Since blood contains ions, we can infer speed of blood flow if we place a test subject in a known magnetic field and measure the resulting current. Suppose a blood vessel is 2.0 mm in diameter, the magnetic field is T, and the measured emf is 0.10 mV. What is the flow velocity of blood?

Example Try it first

Applications Generators Animal navigation Solid waste recycling Burglar alarms Metal detectors Speakers Seismometers Ground-fault circuit interrupters Computer memory Inductive chargers Etc.

Transformers It is more efficient to carry electricity long distances at high voltage. However, high voltage can be very dangerous so is less useful in most situations. A transformer is a device for increasing or decreasing the voltage of an alternating current (ac).

Understanding transformers Alternating current in primary coil results in changing magnetic field in iron core Changing magnetic field induces current in secondary coil Changing magnetic field propagates through iron core.

Physics of transformers

More…

Example The charger for a cell phone contains a transformer that reduces 120-V alternating current to 5.0 V ac. Suppose the secondary coil contains 30 turns and the charger supplies 700 mA. How many turns in the primary coil? Try it first

Example The charger for a cell phone contains a transformer that reduces 120-V alternating current to 5.0 V ac. Suppose the secondary coil contains 30 turns and the charger supplies 700 mA. What is the current in the primary coil? Try it first

Example The charger for a cell phone contains a transformer that reduces 120-V alternating current to 5.0 V ac. Suppose the secondary coil contains 30 turns and the charger supplies 700 mA. How much power is transformed? Try it first

Typical power lines

Lenz’s Law

Electromagnetic waves A changing electric field can induce a magnetic field. A changing magnetic field can induce an electric field. Therefore, it should be possible to create a self-sustaining electric and magnetic field independent of charges or currents! A changing electric field creates a magnetic field which then changes in just the right way to recreate the electric field which changes to recreate the magnetic field… etc. These are electromagnetic waves (more about which to come).