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Flashcards · AP® Physics 2: Algebra-Based · Unit 12

Unit 12: Magnetism and Electromagnetism flashcards

28 cards on topics 12.1 to 12.4. Pick a topic or study the whole unit.

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12.1 Magnetic Fields

Can a magnet have a single pole?
No. Magnetic fields come from dipoles, never a lone pole. Cutting a bar magnet gives two smaller dipoles, each with N and S ends.
Which way does the magnetic field point?
The way the north end of a compass points. Outside a bar magnet it runs from N to S; inside, from S to N. Field lines are closed loops and never cross.
Is Earth's magnetic pole in the Arctic a north pole?
No. Earth is modelled as a dipole, and the magnetic pole near the geographic North Pole is a magnetic south pole, which attracts the north end of a compass.
What causes magnetism in materials?
Moving charge: electrons orbiting and spinning in atoms form magnetic dipoles. Permanent and induced magnetism are both alignment of these dipoles.
How do ferromagnetic, paramagnetic and diamagnetic materials differ?
Ferromagnetic (Fe, Ni, Co): domains align, strong attraction, can stay magnetised. Paramagnetic (Al): weak attraction, lost afterwards. Diamagnetic (Cu, water): weak repulsion.
How do you add two perpendicular magnetic fields?
B_total is the vector sum: B = √(B₁² + B₂²), at an angle tan⁻¹(B₁/B₂) from B₂.
What is the vacuum permeability?
μ₀ = 4π × 10⁻⁷ T·m/A ≈ 1.26 × 10⁻⁶ T·m/A, a constant. A material's permeability μ is not constant and varies with temperature and field strength.

12.2 Magnetism and Moving Charges

What is the magnetic force on a moving charge?
F_B = qvB sin θ, at right angles to both v and B. It is zero for a charge at rest or moving parallel or antiparallel to B.
How do you use the right-hand rule for the force on a moving charge?
Fingers along v, curl towards B, thumb gives the force on a positive charge. Reverse the direction for a negative charge such as an electron.
Why does a charge moving perpendicular to a uniform magnetic field move in a circle?
The force is always perpendicular to v, so it does no work and the speed is constant. Radius r = mv/(qB); period T = 2πm/(qB), independent of speed.
A particle's speed is tripled in the same magnetic field. How does the radius of its circle change?
It triples, because r = mv/(qB) ∝ v.
What is a velocity selector?
Crossed E and B fields whose forces on a charge are opposite. Only particles with v = E/B pass undeflected, whatever their charge or mass. E = 4.0 × 10⁴ V/m and B = 0.20 T select 2.0 × 10⁵ m/s.
What is the Hall effect?
In a conductor in a magnetic field, the sideways force pushes carriers to one edge, creating a potential difference ΔV_H = vBw across the width w (v = drift speed) once the forces balance.
What is the magnetic field of a moving charge like?
At a point, B is perpendicular to both v and the line from the charge to the point. It is stronger for faster charges and closer points, and zero straight ahead or behind.

12.3 Magnetism and Current-Carrying Wires

What does the magnetic field around a long straight wire look like?
Circles centred on the wire, with B tangent to them. Thumb along the current, fingers curl the way B goes: current into the page gives clockwise circles.
What is the magnetic field of a long straight wire?
B = μ₀I/(2πr), with μ₀/(2π) = 2 × 10⁻⁷ T·m/A. B ∝ I and B ∝ 1/r (not 1/r²). At 2.0 cm from 3.0 A, B = 3.0 × 10⁻⁵ T.
What is the force on a current-carrying wire in a magnetic field?
F = IℓB sin θ, with ℓ the length in the field and θ between the current and B. Largest when the wire is perpendicular to B; zero when parallel.
Do parallel wires carrying current attract or repel?
Same direction: attract. Opposite directions: repel. The forces are a third-law pair, equal and opposite, with F/ℓ = μ₀I₁I₂/(2πd).
A 0.10 m wire carries 2.0 A at right angles to a 0.50 T field. What is the force?
F = IℓB = 2.0 × 0.10 × 0.50 = 0.10 N, perpendicular to both the wire and the field.
Which way is the field at the centre of a current loop?
Along the loop's axis. Curl your right-hand fingers with the current; the thumb gives B.

12.4 Electromagnetic Induction and Faraday’s Law

What is magnetic flux?
Φ = BA cos θ, in webers (1 Wb = 1 T·m²), with θ measured from the area vector (perpendicular to the surface), not from the surface. Flux changes if B, A or θ changes.
What is Faraday's law?
A changing flux induces an emf: ε = −ΔΦ/Δt, or |ε| = N|ΔΦ|/Δt for a coil of N turns. A steady flux, however large, induces no emf.
How do you apply Lenz's law?
Find the external B through the loop; decide if flux is increasing or decreasing; the induced field opposes B if increasing and matches B if decreasing; then the right-hand rule gives the current.
Why is Lenz's law a consequence of energy conservation?
The induced current opposes the change, so work must be done against it, and that work becomes electrical energy. If it aided the change, energy would be created.
What is the emf of a rod moving through a magnetic field?
ε = Bℓv, for a rod of length ℓ moving at speed v perpendicular to B. In a closed circuit I = ε/R, and the magnetic force on the rod opposes its motion.
How do you read induced emf from a flux–time graph?
The emf is minus the slope: a straight rise gives a constant emf of one sign, flat gives zero, a straight fall gives the opposite sign, and steeper means larger.
The flux through each turn of a 100-turn coil changes by 2.0 × 10⁻³ Wb in 0.050 s. What is |ε|?
|ε| = N|ΔΦ|/Δt = 100 × 2.0 × 10⁻³ / 0.050 = 4.0 V.
Does an open loop have an induced emf?
Yes. A changing flux induces an emf even in an open loop, but a current flows only in a closed circuit.

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