# 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

• 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