Untitled

• Magnetism is explored including magnetic fields, forces, and fluxes.
• Electromagnetism, Faraday's Law, Lenz's Law, Biot-Savart Law, and Ampere's Law are covered.
• Consideration is given to induced electric fields and AC & LC circuits.

Magnetic Poles

• These are the parts of magnets where the magnetic field is strongest.
• Magnetic field/force weakens with distance from the poles.
• Magnets always exist as dipoles (North and South poles).
• Magnetic monopoles do not exist.
• Unlike poles attract, while like poles repel.

Magnetization & Demagnetization

• Magnetic properties diminish over time or through demagnetization.
• Demagnetization methods include hammering, heating, and exposure to alternating current.
• These methods disrupt molecular alignment, canceling the material's polarity.
• Magnetization can restore polarity by realigning molecules.
• Demagnetized magnets can be remagnetized by exposure to a strong magnetic field.
• Magnet types: Permanent, natural, temporary, and electromagnets.
• Demagnetization can be achieved through hammering, burning/heating, and exposure to alternating current.

Magnetic Field

• This is the area around a magnet where magnetic force is exerted.

Magnetic Field Lines

• These lines represent magnetic fields in continuous loops.
• Outside a magnet, field lines exit the north pole and curve towards the south pole.
• Inside a magnet, field lines move straight from south to north.
• Arrangement is three-dimensional, curving around the magnet.
• Near the poles, magnetic field lines are entering the south pole and leaving the north.
• Closer spacing indicates a stronger magnetic field and further spacing indicates a weaker field.
• Closer to the source the magnetic field is stronger.
• Farther from the source the magnetic field is weaker.

Oersted Discovery

• Hans Cristian Oersted's discovery led to the concept of electromagnetism.

Electromagnetism

• Moving electric charges (current) create a magnetic field perpendicular to the current flow.
• No magnetic field exists when the current is off.
• Current, magnetic field, and magnetic force are interrelated.
• Electromagnets are conductors of current.

Magnetic Field Formula

• Describes the magnitude of the magnetic field.
• Mag field magnitude = (permeability of free space)(current magnitude) / 2π(distance)
• B = (µ₀I) / (2πr)
  • B = magnetic field magnitude (Tesla, T)
  • µ₀ = permeability of free space (4π x 10⁻⁷ T·m/A)
  • I = magnitude of the electric current (Amperes, A)
  • r = distance (m)
• 1 Tesla = 1x10⁴ Gauss (G) or 10,000 G

Right Hand Grip Rule

• Used to find the direction of magnetic field (B) and current (I).
  • Thumb points in the direction of the current.
  • The curve of the four fingers indicates the direction of the magnetic field.
• A dot represents current coming out of the page towards the viewer.
• A cross represents the current going into the page away from the viewer.

Magnetic Force

• Magnetic force is caused by the motion of charges and is a consequence of the electromagnetic force.
• A magnetic field results in magnetic force; without a magnetic field, there is no magnetic force.
• Objects containing charges moving in the same direction attract.
• Objects with charges moving in opposite directions repel.
• The magnitude of the magnetic force depends on the amount of charge (q) in motion (v) in each object and how far apart they are (B).

Magnetic Force Formula

• Describes a charge particle moving in a magnetic field.
  • FM = qvB; FM = qvB sinθ
    • q = charge (C)
    • v = velocity of the charge (m/s)
    • B = strength of magnetic field (Tesla, T = N/A·m)
• Magnetic force is proportional to q and the magnitude of the vector cross product q x B.

Right Hand Rule (RHR)

• Determines the direction of the magnetic force.
  • Thumb: direction of the force (Fᴍ)
  • Index finger: direction of the moving charges/current (v)
  • Middle finger: direction of the magnetic field (B)

Movement of Particles in a Mag Field

• Charge moves in circular motion when placed in a magnetic field.
• A magnetic field influences moving charges.
• Electrons, being moving charges, experience force in a magnetic field.
• Charged particles entering a magnetic field perpendicularly experience force at right angles and move in a circular path.
• The radius of this circle is given by R = mv/qB
  • m = mass
  • v = velocity
  • q = charge
  • B = magnetic field
• Radius calculation: Dividing the product of a particle's mass and velocity by the product of its charge and magnetic field magnitude.

Cyclotron Formula

• Determines the number of rotations a charged particle makes in a magnetic field.
• f = qB / 2πη
  • f = Frequency, Hertz (Hz)
  • q = absolute value of the charge, Coulombs (C)
  • B = magnetic field strength, Tesla (T)
  • m = mass of the particle (kg)
• The standard unit is Hertz (Hz), named after German physicist Heinrich Hertz.

Magnetic Flux

• Represents the total number of magnetic field lines passing through a coil or area.
  • фв = BAcosθ
    • B = magnetic field, Tesla (T)
    • A = surface area, m²
    • θ = angle between the area vector/normal to the surface and magnetic field.
• Unit: T · m² = Weber (Wb)
• If the surface or coil is perpendicular to the magnetic field lines: θ = 0° or 180°; Фв = max
• If the surface or coil is parallel to the magnetic field lines: θ = 90°; Фв = 0
• If the surface or coil is at a certain angle from the magnetic field lines: θ = given angle; фв = less than maximum

Magnetic Force on a Current-carrying Wire

• A current-carrying wire in a magnetic field experiences a magnetic force.
  • FB = ILXB; FB = ILxBsinθ
    • FB = magnetic force, N
    • I = current, A
    • L = length of the wire, m
    • B = magnetic field, T
• Use the Palm method or RHR2 to determine the direction.

PALM METHOD

• Palm: direction of the magnetic force
• Thumb: direction of the current
• 4 fingers: direction of the magnetic field

Faraday's Law

• Defines electromotive induction in a closed loop.
• The induced electromotive force equals the negative rate of change of magnetic flux inside the loop: ε = - ΔΦB/Δt
  • ε = - (ФBf — ФBi)/Δt
• For multiple coils, the EMF is multiplied by the number of coils (N): ε = -N ΔΦB/Δt

Factors Changing The Induced EMF

• Change in B, A, or θ of B & A and number of coils (N) and time

Changing the Magnetic Flux

• Change the magnetic field to change the magnetic flux.
• Movement is required to change magnetic field according to Faraday's Law.
• Without movement, there won't be induced EMF/current.
• Step up the output voltage is higher than the input and Step down the output voltage is lower than the input.

Lenz's Law

• "The direction of the induced current is such that its own magnetic field opposes the change that induced it."
• Faraday's Law: ε = -N d(фв)/dt
• The minus sign means the induced emf will always oppose the change.
• Induced emf produces a magnetic field to oppose the original change in the magnetic flux.
• Lenz's law guides figuring out current direction in a loop.
• It helps in remembering that the induced emf has an induced current, so there is also an induced magnetic field.
• An induced magnetic field does not create nor add energy to a system.
• When the magnetic field is already increasing, the induced magnetic field prevents energy from being added on and on.

Moving a Magnet Near a Coil

• The change in Bind occurs to keep the flux in the loop constant.

Biot-Savart Law

• Determines the magnetic field at a point due to a current; Use Jean-Baptiste Biot and Felix Savart's law.
• Predicts the magnetic field at point P (distance r) from current I.
• Applicable in asymmetrical problems.
• Steps:
  • Calculate the magnetic field generated by a current element
  • Sum up the magnetic fields generated by a multitude of current elements at the same point.
• For an infinitely long, straight wire carrying a current I, the magnetic field at a point P and a distance a away from the wire: dB = (µ₀I) / (2πa)
  • µ₀ = permeability (4πx10−7 Tm/A)
  • I = current, A
  • a = distance, m

The Magnetic Field at the Center of a Circular Current Loop

• dB = (µ₀NI) / (2a)
  • µ₀ – permeability (4πx10−7 Tm/A)
  • N - number of turns
  • I - current, А
  • a – radius of the circle, m

The Magnetic Field at the Center of a Very Long Solenoid

- B  = (µ₀NI) / L == µ₀nI
    - µ₀ – permeability (4πx10−7 Tm/A)
    - N/L = n - number of turns per length
    - N - number of turns
    - L - length of the wire
    - I - current, A

Ampere's Law

• Given by Andre-Marie Ampere (1826).
• "For any closed loop, the dot product of the magnetic field and the total distance (length elements) around the loop is equal to the product of the permeability constant and current enclosed by the loop.”
• Applied in problems with high symmetry.
• For straight current carrying wire with a circular loop, the magnetic field generated by any current element or wire segment is the same.
  • Sum all current carrying elements around the path to get the circle's circumference.
  • ØB dl = µ₀Ienc ; B(2πr) = µ₀I

Biot-Savart Law Vs. Ampere's Law

• Ampère's Law is a more general form derived from Biot-Savart and simplifies calculations in symmetrical situations.
• Both laws give consistent results when correctly applied.
• Ampère's Law is more generalized and convenient in certain cases.

Electrostatic F. Vs Induced E. Fields

Electrostatic Fields

• Start at positive charges, end at negative; conservative field

Induced E. Fields

• Non-electrostatic, don't start/end at a charge, non-conservative, require varying magnetic field, with or without free electrons

AC & LC Circuits

Alternating Current

• Safe to transfer over longer city distances and can provide more power.
• Direction reverses while flowing in a circuit: Time-varying magnitude.
• Electrons keep switching directions - forward and backward.
  • Obtained from A.C Generator and mains.

Direct Current

• Frequency of zero and flows in one direction in the circuit.
• Constant magnitude: Electrons steadily move in one direction or 'forward'.
• Obtained from Cell or Battery

Inductance

• The device placed in a circuit to oppose a change in current; that is, to maintain, and regulate, a steady current in that section of the circuit (solenoid).
  • An inductor: Slows down the increase of current (back emf).
  • Current (steady) constant magnetic field = no emf
• L = (ΝΦв) / i

Inductance, L

- The tendency of an electrical conductor to oppose a change in the electric current flowing through it.
   - ↑ inductance, ↑ ability to oppose change
    - Unit: Henry, H (Weber/Ampere).
       - Self and Mutual Inductance

Self Inductance

- L = ((µ₀N²A) / l
    - L – inductance, Henry (Weber/Ampere)
     – diameter of the coil in meters, permeability of free space ((4πx10−7 Tm)/
    - N – number of turns in the coil
    - A – cross-sectional area
    - l – length of the coil in meters

Mutual Inductance

• Need another inductor to induce back emf: M = (№2ΦB (2)) / (i( 1)) = (№2ΦB (1)) / (i( 2))
• SI Unit: H (Weber/Ampere)
• For the induced emfs: -M * (di(1))/(dt) and 1; ε = -M * (di(2))/(dt);
• Unit: V

Transformers

• Device used to step up or step down voltage (lifeblood is Mutual Inductance):
  • Step-down transformer the output voltage is lower than the input voltage.
  • Step-up transformer the output voltage is higher than the input voltage.

LC Circuits

Sometimes called oscillatory circuit, contains an inductor and a capacitor. When a charged capacitor is connected to an inductor, energy oscillates from electrical to magnetic, and back to electrical, and so on.