Understanding Electromagnetic Induction: Faraday's Law and Applications, Exercises of Physics

Download Understanding Electromagnetic Induction: Faraday's Law and Applications and more Exercises Physics in PDF only on Docsity!

ElectroMagnetic Induction^ AP Physics B

What is E/M Induction? Electromagnetic Induction is theprocess of using magnetic fields toproduce voltage, and in acomplete circuit, a current.^ Michael Faraday

first discovered it, using some of the works of Hans Christian Oersted. His work started at first using different combinations ofwires and magnetic strengths and currents, but it wasn't until he tried

moving

the wires that he got any success.It turns out that electromagnetic induction is created by just that -

the moving

of a conductive substance through a magnetic field.

Magnetic Flux The first step to understanding the complex nature ofelectromagnetic induction is to understand the ideaof^ magnetic flux.^ Flux is a general termassociated with a FIELD that isbound by a certain AREA. So^ MAGNETIC FLUX

is any^ AREA that has a^ MAGNETIC FIELD passing through it.

B^ A

We generally define an AREA vector as one that is perpendicular to thesurface of the material. Therefore, you can see in the figure that theAREA vector and the Magnetic Field vector are

PARALLEL. This then

produces a^ DOT PRODUCT

between the 2 variables that then define flux.

Magnetic Flux – The DOT product

Wb) or Weber(Tm: cos^2 Unit AB^ θ BA

• =Φ B =Φ B How could we CHANGE the flux over a period of time?
  We could move the magnet away or towards (or the wire)
  We could increase or decrease the area
  We could ROTATE the wire along an axis that is PERPENDICULAR to thefield thus changing the angle between the area and magnetic field vectors.

Useful Applications The Forever Flashlight uses the Faraday Principle ofElectromagnetic Energy to eliminate the need for batteries. TheFaraday Principle states that if an electric conductor, like copperwire, is moved through a magnetic field, electric current will begenerated and flow into the conductor.

Useful Applications

AC Generators use Faraday’slaw to produce rotation andthus convert electrical andmagnetic energy intorotational kinetic energy.This idea can be used torun all kinds of motors.Since the current in the coilis^ AC,^ it is turning on andoff thus creating aCHANGING magnetic fieldof its own. Its ownmagnetic field interfereswith the shown magneticfield to produce rotation.

Microphones

A microphone works when soundwaves enter the filter of amicrophone. Inside the filter, adiaphragm is vibrated by thesound waves which in turn movesa coil of wire wrapped around amagnet. The movement of the wirein the magnetic field induces acurrent in the wire. Thus soundwaves can be turned intoelectronic signals and thenamplified through a speaker.

Example A coil with 200 turns of wire is wrapped on an 18.0 cm square frame.Each turn has the same area, equal to that of the frame, and thetotal resistance of the coil is 2.

Ω^. A uniform magnetic field is

applied perpendicularly to the plane of the coil. If the field changesuniformly from 0 to 0.500 T in 0.80 s, find the magnitude of theinduced emf in the coil while the field has changed as well as themagnitude of the induced current.= ==^ =

∆Φ= IIR I

BANt x

BN t^ )^2 (

90 cos) 18. 018. 0 )( 0500. 80. 0

cos 0 ( 200 ε ε ε

θ ε^ 4.05 V 2.03 A

Why did you find theABSOLUTE VALUE of theEMF?What happened to the “ – “that was there originally?

Lenz’s Law & Faraday’s Law

∆Φ BN −= t^ ∆

ε Let’s consider a magnet with it’s north pole movingTOWARDS a conducting loop.DOES THE FLUX CHANGE?DOES THE FLUX INCREASE OR DECREASE?WHAT SIGN DOES THE “

∆” GIVE YOU IN FARADAY’S LAW?DOES LENZ’S LAW CANCEL OUT? What does this mean?

Yes! IncreasePositiveNO

Binduced This means that the INDUCED MAGNETIC FIELD around the WIRE causedby the moving magnet OPPOSES the original magnetic field. Since theoriginal B field is downward, the induced field is upward! We then use thecurling right hand rule to determine the direction of the current.

Lenz’s Law A magnet isdropped down aconducting tube.

The INDUCED current creates an INDUCEDmagnetic field of its own inside the conductorthat opposes the original magnetic field.The magnet INDUCES acurrent above and below themagnet as it moves.

Since the inducedfield opposes thedirection of theoriginal it attractsthe magnet upwardslowing the motioncaused by gravitydownward.

If the motion of the magnet were NOT slowed this would violate conservation of energy!

In summary Faraday’s Law

is basically used to find the MAGNITUDE of the induced EMF. Themagnitude of the current can then be foundusing Ohm’s Law provided we know theconductor’s resistance. Lenz’s Law

is part of Faraday’s Law and can help you determine the direction of thecurrent provided you know HOW the flux ischanging

Motional EMF – The Rail Gun A railgun consists of two parallel metal rails (hence the name) connected to anelectrical power supply. When a conductive projectile is inserted between the rails(from the end connected to the power supply), it completes the circuit. Electronsflow from the negative terminal of the power supply up the negative rail, across theprojectile, and down the positive rail, back to the power supply.

In accordance with the right-hand rule,the magnetic field circulates aroundeach conductor. Since the current is inopposite direction along each rail, thenet magnetic field between the rails (

B ) is directed vertically. In combination withthe current ( I ) across the projectile, thisproduces a magnetic force whichaccelerates the projectile along the rails.There are also forces acting on the railsattempting to push them apart, but sincethe rails are firmly mounted, they cannotmove. The projectile slides up the railsaway from the end with the powersupply.

Motional EMF

In the figure, we areapplying a force this timeto the rod. Due to Lenz’sLaw the magnetic forceopposes the appliedforce. Since we knowthat the magnetic forceacts to the left and themagnetic field acts intothe page, we can use theRHR to determine thedirection of the currentaround the loop and theresistor.

Example An airplane with a wing span of 30.0 m flies parallel to the Earth’ssurface at a location where the downward component of theEarth’s magnetic field is 0.60 x

-4^ T. Find the difference in

potential between the wing tips is the speed of the plane is 250m/s.^ = =^ =

− ε ε ε

) (^250) )( (^30) ( Blv^41060. 0^ x^ 0.45 V In 1996, NASA conducted an experiment with a 20,000-meter conductingtether. When the tether was fully deployed during this test, the orbitingtether generated a potential of 3,500 volts. This conducting single-linetether was severed after five hours of deployment. It is believed that thefailure was caused by an electric arc generated by the conductive tether'smovement through the Earth's magnetic field.