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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