Chapter 5 - Magnetism and Electromagnetic Induction

Magnetic Fields

All magnets have South and North poles
* If you took a magnet such as a rectangular-shaped bar magnet, you are not separating the poles - you are creating two magnets that still have North and South poles
Magnetism and static electricity
  * Similarities:
    * Magnets and charges exert equal and opposite forces on each other
    * Magnetic and electric fields extend into infinity and get weaker with increased distance
  * Differences:
    * Magnetic fields only affect moving charges whereas electric fields can affect both stationary and moving charges
    * The force exerted by magnetic fields is perpendicular to both the velocity of the charge and the direction of the magnetic field
    * Magnetic field lines are loops instead of lines like in electric fields
Magnetic Field lines
* Magnetic field lines are loops that point away from the North and toward the South

Magnetic field lines around a bar magnet

* Iron filings gather on these magnetic field lines, creating patterns visible to the human eye
* Like electric field lines, longer arrows indicate larger field strength

What creates magnetic fields?
  * Moving charges
    * For bar magnets, these charges are the electrons circling the nucleus of atoms
    * In wires, current serves as moving charges
3-D nature
  * Magnetic fields are 3D which is often hard to show on paper
  * In the exam, a dot with a circle (the circle is most often there but it could just be a dot) around it indicates a magnetic field coming out of the page (think of an arrow head coming at you)
    * An X indicates a magnetic field going into the page (think of the back of an arrow)

Applications of Magnetic Fields

Dipoles of the Earth
* The magnetic south pole is actually the geographic north pone and vice versa
The magnetic field in a straight wire with current
  * The magnetic field forms circles in the plane perpendicular to the length of the wire
    * Picture washers on a wire - those represent circles of the magnetic field
  * __The right-hand rule__

    * Grasp a pencil with your right hand
    * Your fingers will curl around the pencil in the same direction the magnetic field curls
      * If you imagine a wire with current pointing left, the magnetic field will be represented with X’s on top of the wire and dots below the wire (also known as counterclockwise)
    * Your thumb will point in the direction of the current
  * ==B = 𝜇I/(2πr)==
    * B: magnetic field
    * 𝜇: vacuum permeability (4π x 10^-7)
    * I: Current
    * r: distance between enter of wire to where you’re trying to find the field strength

Solenoid
* __Solenoid__: a coil of wire created by wire looped circularly multiple times
* Solenoids hooked up to a battery creates a dipole magnetic field like a bar magnet
Force on a moving charge
  * If the velocity of a moving particle is perpendicular to the magnetic field, a magnetic force is exerted on the moving charge
  * ==F = qvBsin(θ)==
    * F: magnetic force
    * q: charge of particle
    * v: velocity
    * B: magnetic field
    * θ: angle between velocity and magnetic field vectors
  * __Right hand rule - “flat finger” rule__

    * Fingers point in the direction of the magnetic field
    * Thumb points in the direction of the velocity for the positive charge
    * Palm points in the direction of the force
    * The right hand rule works for positive particles but for negative particles, the same rules apply if you use your left hand
  * When acceleration is perpendicular to the velocity, as is the case because the magnetic force is perpendicular to the velocity, the acceleration is centripetal

Force on a current-carrying wire from an outside magnetic field
  * ==F = ILsin(θ)B==
    * F: magnetic force
    * L: length of the wire
    * B: magnetic field
    * I: current
    * θ: angle between the current and magnetic field
The force between two parallel wires
  * To solve problems like this, find the directions of the magnetic field around Wire B and determine the effects on Wire A
  * The forces on the wires are equal and opposite in direction
  * ==B = 𝜇I/(2πr)==
    * B: Magnetic field from wire B
    * I: Current from wire B
    * r: distance between wires A and B
  * ==F = ILsin(θ)B==
    * F: magnetic force on wire A from wire B
    * I: current through wire A
    * L: length of wire (lengths of wire A and B are the same)
    * B: magnetic field from wire B
Mass Spectrometer
Remember that magnetic forces give charges a centripetal acceleration
* This means the magnetic force only changes the direction of the charge without altering the magnitude of the velocity
* The path of the charge then becomes circular
Fc = Fb
* Fc: centripetal force
* Fb: magnetic force
==mv^2/r = qvB==
  * m: mass of the particle
  * v: velocity
  * r: radius of the circular path
  * q: charge
  * B: magnetic field
  * Therefore, ==r = mv/(qB)==
If part of the velocity is parallel to the field (theta is not 90 degrees), the charge will take a helical path
__Mass Spectrometer__: a device used to determine the charge to mass of a particle by arcing them in a magnetic field and finding the radius of its path

Magnetic Flux

__Magnetic Flux__: a measure of the magnetic field passing through an area
* Measured in Webers
Magnetic field strength (magnetic flux density) multiplied by area is equal to magnetic flux
  * ==ɸ = Bcos(θ)A==
  * ɸ: magnetic flux
  * B: magnetic field
  * θ: angle between the magnetic field and the “window” of magnetic flux we’re measuring

Electromagnetic Induction

Electromotive force
  * ==ε = Blv==
    * ε: electromotive force
    * B: magnetic field
    * l: length of the wire in the magnetic field
    * v: velocity of the wire
  * The movement of a wire through a magnetic field can produce an electromotive force
  * Other ways to use electromagnetic induction:
    * Changing magnetic field strength
    * Changing the flux area of a loop
    * Turning the loop
  * ==ε = -N(Δɸ/Δt)==
    * N: number of turns in the wire around the loop
  * For rectangular loops:
    * ==ε = BLv==
      * ε: electromotive force
      * L: length of the rectangle side that is entering the magnetic field
      * B: magnetic field
      * v: velocity
__Lenz’s Law__: The direction of the induced current opposes any change in flux
* If we move a loop with zero magnetic field near a magnetic field coming out of the page, the induced current will create a magnetic field into the page within the loop to oppose the increased magnetic field out of the page
* When the loop stops moving and is completely in the region with the magnetic field, there is no induced emf with no changing flux
Uses for electromagnetic induction:
  * Generation of electricity
  * In microphones and speakers
  * To run motors
  * In MRIs
  * On credit cards
  * Point is: electromagnetic induction is very important in everyday use

Magnetic Behavior

Ferromagnetism
  * Ex: iron, nickel. and cobalt
  * Localized regions called domains are inside this material
  * In an external magnetic field, the domains align, amplifying it
    * Domains can grow enough to create a permanent magnet
  * Magnets strongly attract ferromagnetic materials
Paramagnetism
  * Unlike ferromagnetic materials, paramagnetic materials don’t form permanent magnets
  * Magnets weakly attract paramagnetic materials
  * The domains still align with the external magnetic field
Diamagnetism
  * Internal properties align opposite to the external field - cancel out that part of the magnetic field
  * Ex: water, graphite
  * Magnets weakly repel diamagnetic materials