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Flashcards · AP® Physics C: Electricity and Magnetism · Unit 12

Unit 12: Magnetic Fields and Electromagnetism flashcards

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

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12.1 Magnetic Fields

What is a magnetic field?
A vector field B, measured in tesla, that gives the magnetic force on moving charges, currents and magnetic materials. A charge at rest feels no magnetic force.
What are the sources of magnetic fields?
Dipoles or combinations of dipoles, never monopoles. Every dipole has an N and an S pole; cutting a magnet gives two dipoles. Dipoles come from the circular or spinning motion of charge, mainly electrons.
What is Gauss's law for magnetism?
∮B·dA = 0 for every closed surface, because there are no magnetic monopoles. Field lines do not end at the S pole; they continue through the magnet.
How does a compass respond to a magnetic field?
It is a small dipole that turns so its N end points along B. The pole near Earth's geographic North Pole is a magnetic south pole.
What are ferromagnetic, paramagnetic and diamagnetic materials?
Ferromagnetic: μ much greater than μ₀, strongly magnetized. Paramagnetic: μ slightly greater than μ₀, weakly attracted. Diamagnetic: μ slightly less than μ₀, weakly repelled; all materials have it.
Why is an unmagnetized paper clip attracted to either pole of a magnet?
The field induces aligned dipoles in it, with the near end opposite to the nearby pole, so it is always attracted.
How do you find a missing flux through part of a closed surface?
Net flux through any closed surface is zero, so the flux through the last part is minus the sum of the fluxes through all the other parts (entering counts as negative).
What is the permeability of free space?
μ₀ = 4π × 10⁻⁷ T·m/A, a constant. A material's permeability μ depends on composition and can change with temperature, orientation and field strength.

12.2 Magnetism and Moving Charges

What is the magnetic force on a moving charge?
F = q(v × B), size |q|vB sin θ. It is perpendicular to both v and B. A charge at rest or moving along B feels no force. Reverse the right-hand-rule direction for a negative charge.
Why does a magnetic force not change a charge's speed?
It is always perpendicular to the velocity, so F·v = 0 and it does no work. It only changes the direction of motion.
What are the radius and period of a charge's circle in a uniform magnetic field?
r = mv/(|q|B) and T = 2πm/(|q|B). The period does not depend on speed. Doubling both v and B leaves r unchanged.
What path does a charge follow when v is at an angle to a uniform B?
A helix. Only v⊥ goes into the radius r = mv⊥/(|q|B); the pitch is v∥ × T.
What speed passes undeflected through crossed electric and magnetic fields?
v = E/B, where the electric force qE balances the magnetic force qvB. With both fields, F = qE + q(v × B).
What is the magnetic field of a moving point charge?
B = (μ₀/4π) q(v × r̂)/r², size (μ₀/4π)qv sin θ/r², with r̂ from the charge to the point. B circles the line of motion and is zero along it.
What is the Hall effect?
In a magnetic field, carriers in a current-carrying strip are pushed to one edge, creating a potential difference across its width: ΔV_H = v_dBw = IB/(nqt), where t is the thickness along B.
A proton moves at 2.0 × 10⁶ m/s at 30° to a 0.50 T field. What is the force on it?
F = qvB sin θ = 1.60 × 10⁻¹⁹ × 2.0 × 10⁶ × 0.50 × 0.50 = 8.0 × 10⁻¹⁴ N.

12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law

What is the Biot-Savart law?
dB = (μ₀/4π) I dℓ sin θ / r², in the direction of dℓ × r̂. The total field is the integral over the whole wire. A piece aimed straight at the point contributes nothing.
What is the field of a long straight wire?
B = μ₀I/(2πr), in circles centred on the wire, given by the right-hand rule. It has no component toward, away from or along the wire.
What is the field at the center of a circular loop or arc?
Loop of radius R: B = μ₀I/(2R), times N for N turns. Arc of angle φ in radians: B = μ₀Iφ/(4πR). A quarter circle gives μ₀I/(8R).
What is the field on the axis of a current loop?
B = μ₀IR²/[2(R² + z²)^(3/2)], along the axis. Only axial components survive. Far away (z much larger than R), B ≈ μ₀IR²/(2z³).
What is the field of a finite straight wire on its perpendicular bisector?
B = μ₀IL/[2πa√(L² + 4a²)] at distance a. For L much larger than a, this tends to μ₀I/(2πa).
What is the force on a current-carrying wire in a magnetic field?
F = Iℓ × B, size IℓB sin θ, for a straight wire; F = ∫I dℓ × B for a curved one. The net force on a closed loop in a uniform field is zero.
What is the force between two parallel wires?
F/ℓ = μ₀I₁I₂/(2πd). Currents in the same direction attract; opposite directions repel.

12.4 Ampère’s Law

What does Ampère's law state?
∮B·dℓ = μ₀I_enc: the line integral of B round a closed loop equals μ₀ times the net current through it. Curl right fingers along the path; current along the thumb is positive.
When can Ampère's law give B directly?
Always true, but useful only when symmetry makes B constant and parallel to parts of the loop and perpendicular or zero on the rest: long straight wires, long solenoids, slabs and cylinders.
What is the field inside a long solenoid?
B = μ₀nI, where n = N/L is turns per metre, uniform inside and nearly zero outside for an ideal solenoid. 1000 turns per metre at 2.0 A gives about 2.5 × 10⁻³ T.
What is the field inside a uniform solid wire carrying current?
B = μ₀Ir/(2πR²) inside, rising linearly with r because I_enc = Ir²/R². Outside, B = μ₀I/(2πr).
How do you use Ampère's law when current density varies with radius?
Integrate: I_enc = ∫₀ʳ J(r′)2πr′ dr′, then B = μ₀I_enc/(2πr). Do not use J × area.
What is the field inside an empty conducting tube or outside a coaxial cable?
Zero, because the net current enclosed by a coaxial Amperian circle is zero.
What is the field of a current-carrying slab?
Outside: B = μ₀Jt/2, independent of distance. Inside, at distance z from the mid-plane: B = μ₀Jz.
Does ∮B·dℓ = 0 mean B = 0 on the loop?
No. It means zero net enclosed current. Opposite currents through the loop subtract.

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