12.1 Magnetic Fields

A magnetic field is a vector field (B) that tells you the magnetic force on moving charges, currents, or magnetic materials. It comes from magnetic dipoles (like aligned electron orbits/spins)—never isolated monopoles—so field lines form closed loops and outside a bar magnet they go from the north to south pole. In AP terms: dipoles produce B, a compass aligns with B, and ferromagnetic, paramagnetic, and diamagnetic materials respond differently. How it “works”: a charge q moving with velocity v feels the Lorentz force F = q(v × B)—direction given by the right-hand rule and magnitude qvB sinθ—so the force is perpendicular to v and B (it changes direction, not speed). Changing B or a moving loop changes magnetic flux and induces emf (Faraday’s law). Free-space permeability μ0 appears in equations like Biot–Savart and Ampère’s law; material permeability varies. For a concise AP review, see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Magnetic field lines always form closed loops because there are no magnetic monopoles—every magnetic source is a dipole with a north and a south end, so field lines leave a north and return to a south (CED 12.1.A.1.i–ii and 12.1.A.2.i). More formally, Gauss’s law for magnetism says the net magnetic flux through any closed surface is zero, which mathematically forces field lines to have no beginnings or ends. Physically, the magnetic moments come from moving charges (electrons in atoms), so the field you map around a bar magnet or a current loop naturally loops back on itself. This is a core Concept in Topic 12.1 and shows up on the exam when you sketch B-field maps or reason about dipoles. For a clear AP-style review, see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and try practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Ferromagnetic, paramagnetic, and diamagnetic describe how a material’s atomic magnetic dipoles respond to an external B-field (CED 12.1.B, 12.1.C): - Ferromagnetic: atoms have magnetic moments that interact and form domains. An external field aligns many domains and the material can become strongly and permanently magnetized (iron, nickel, cobalt). Shows high magnetic permeability and hysteresis; above the Curie temperature the order is lost. (CED 12.1.B.3.i) - Paramagnetic: atoms have permanent dipole moments but no domain coupling. In an external field the dipoles weakly align with the field, increasing B inside the material slightly; alignment disappears when the field is removed (aluminum, titanium, magnesium). (CED 12.1.B.3.ii) - Diamagnetic: all materials have this weak effect (CED 12.1.B.3.iii). Induced currents in electron motion create tiny dipoles that align opposite the applied field, producing a small repulsion. It’s always present but usually very weak compared to para/ferro effects. For more review, see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and practice questions (https://library.fiveable.me/practice/ap-physics-2-revised).

A magnetic dipole is basically anything that has a north and a south end and makes a tiny loop of magnetic field—think of a tiny bar magnet or a compass needle. On the microscopic level, dipoles come from moving charges (electron orbital motion and spin) so each atom can act like a little magnet. Important AP ideas from the CED: dipoles always come in north–south pairs (no monopoles), their external field lines form closed loops, and the field strength falls off with distance. When many atomic dipoles line up you get ferromagnetism (a permanent magnet); if they only align while an external field exists it's induced/paramagnetic; all materials show weak diamagnetism opposite the applied field. A dipole in an external field tends to rotate until it lines up with that field (compass behavior; Earth acts like a dipole). For a clear AP-focused review, see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Electrons moving in circles make magnetism because a loop of moving charge is a magnetic dipole—it produces a magnetic field with closed field lines and a north/south polarity (CED 12.1.A.1 and 12.1.A.1.i). In atoms this comes from two things: electrons orbiting nuclei and electrons’ intrinsic spin. Each circular motion has a magnetic moment (current × area) that’s like a tiny bar magnet (CED 12.1.B.1). In most materials those tiny dipoles point randomly so fields cancel; in ferromagnets many dipoles align into domains and produce a net external field (CED 12.1.B.1.i, 12.1.B.3.i). The Biot–Savart / Ampère ideas connect moving charge/current to the magnetic field shape; Gauss’s law for magnetism implies no isolated magnetic monopoles—dipoles only. This is a core AP topic (Unit 12) and shows up on MCQ/FR tasks about dipoles, fields, and materials. For a quick review see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and extra practice (https://library.fiveable.me/practice/ap-physics-2-revised).

You can’t have just a single north or south pole because magnetic fields come from magnetic dipoles (tiny loops of moving charge), not monopoles. Field lines form closed loops—they leave a “north” end and return at a “south” end—so isolated poles don’t exist (CED 12.1.A.1.i, 12.1.A.2.i). If you cut a bar magnet in half you don’t get a lone north and a lone south; each piece becomes its own dipole with both poles (CED 12.1.B.1.ii). Mathematically this is expressed by Gauss’s law for magnetism (∇·B = 0): the net “magnetic charge” inside any volume is zero. This is a core idea on the AP: magnetic sources are dipoles, field lines are closed, and poles of the same sign repel while opposite poles attract (CED 12.1.B.1.iii). For a quick refresher, check the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

When you break a bar magnet, you get two smaller bar magnets because magnetic poles always come in north–south pairs—there are no isolated magnetic monopoles (CED 12.1.A.1.i, 12.1.B.1.ii). On the microscopic level a magnet’s field comes from many aligned magnetic dipoles (atomic electron motion and domains). Cutting the magnet just creates new ends where the dipoles near the cut rearrange so each piece still has a north and a south. Field lines remain closed loops, now running from the new north to the new south on each piece (CED 12.1.A.2.i–ii). So instead of isolating a single pole, you simply split one dipole-rich object into two dipole magnets. For more review on magnetic dipoles and domain alignment see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) or the full unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-12). Practice problems are at (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: Earth’s field behaves like one big magnetic dipole because the net effect of many tiny atomic and current-related dipoles in Earth’s core sums to a roughly dipole field, but it isn’t a perfect bar magnet. Why that happens (brief). - Moving conductive fluid in the outer core (the geodynamo) creates large-scale electric currents. Those currents produce a magnetic field with a north and south polarity—i.e., a dipole. - Magnetic fields are vector fields with closed field lines (CED 12.1.A). A compass aligns with the local field because a compass is itself a magnetic dipole (CED 12.1.B.2). - The dipole approximation is useful (CED 12.1.B.4) but Earth has tilt, local anomalies, and higher-order multipole terms, and the field slowly changes over time (secular variation). For AP review, Topic 12.1 covers these ideas; see the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) to practice questions on dipoles, field lines, and compass behavior.

Magnetic permeability (μ) measures how much a material becomes magnetized when you apply a magnetic field—basically how well it “lets” magnetic field lines pass through. The CED says vacuum permeability μ0 (μ0 = 4π×10⁻⁷ T·m/A) shows up in equations (Biot–Savart, Ampère’s law, B of a long straight wire), and the permeability of matter differs from μ0 depending on composition (ferro-, para-, diamagnetic) and conditions (temperature, field strength). Why it matters for the AP exam: you should be able to describe what permeability means (12.1.C.1–C.3) and recognize μ0 in formulas that compute B from currents. You won’t need complicated material-dependent numbers on most items, but you should know permeability affects magnetization and that μ0 is a constant that appears in magnetic-field equations. Review Topic 12.1 on the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: it comes down to how the atomic magnetic dipoles interact and stay aligned. Longer: in ferromagnets (iron, nickel, cobalt) groups of atoms form magnetic domains—regions where many atomic dipoles line up because of strong quantum exchange interactions. An external field can align those domains, and because the interactions favor that alignment, they tend to stay aligned even after the field is removed (that’s permanent magnetism and hysteresis). Paramagnets (like aluminum) have individual atomic dipoles that line up only weakly with an external field; thermal motion and weak interactions randomize them again once the field’s gone, so they aren’t permanently magnetized. All materials also show tiny diamagnetic effects opposite to an applied field. Temperature matters too: above a material’s Curie temperature a ferromagnet loses permanent order. For the AP frame, this matches 12.1.B.1–3 (magnetic dipoles, domains, ferromagnetism vs paramagnetism). Review the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) to see these ideas on the exam.

A compass needle is basically a small magnetic dipole (a tiny bar magnet) made from ferromagnetic material whose atomic dipoles (domains) are aligned. When it’s free to rotate in Earth’s magnetic field, the field exerts a torque τ = μ × B on the needle’s magnetic moment μ, which turns the needle until μ lines up with the local magnetic field B (lowest potential energy). Field lines form closed loops and there are no magnetic monopoles, so the needle points along the field from the local “north” direction of the field to the “south.” Earth’s field can be approximated as a dipole field, so compasses give you geographic headings (with declination). This ties directly to CED 12.1.A/B ideas: magnetic dipoles, field lines, and ferromagnetism. For a quick review, see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) to prep for the AP.

μ0 (the vacuum permeability) is just the constant that tells you how magnetic fields relate to currents in free space. Use μ0 when your formula assumes empty space (no magnetic material)—e.g., Biot–Savart and Ampère-law results like - B around a long straight wire: B = μ0 I / (2πr) - B inside an ideal solenoid: B = μ0 n I Its SI unit is N·A⁻² (or T·m/A). If you have material present, replace μ0 with the material’s permeability μ = μ0 μr (μr = relative permeability) because matter changes the magnetization (see CED 12.1.C). Vacuum permeability shows up whenever you derive magnetic field from currents (Lorentz force uses B, but μ0 only appears if you compute B from currents). For AP questions, memorize the common μ0 formulas (wire, solenoid, Biot–Savart/Ampère contexts) and note when a problem says “in free space.” More practice and examples are in the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and unit review (https://library.fiveable.me/ap-physics-2-revised/unit-12).

Think of every magnet as a bunch of tiny magnetic dipoles (little current loops from electrons) that have a north and south end—you can’t get an isolated magnetic monopole (CED 12.1.A.1.i, 12.1.B.1.ii). Field lines leave the north end and return to the south end, forming closed loops (CED 12.1.A.2.i–ii). When two magnets come near, their dipoles and fields interact. Opposite poles (N next to S) let field lines run smoothly from one magnet into the other, reducing the total magnetic field energy and producing a net attractive force. Like poles (N–N or S–S) force field lines to oppose each other, increasing energy; the system lowers energy by pushing the magnets apart, so they repel (CED 12.1.B.1.iii, 12.1.B.1.iv). You can also picture each magnet as a tiny compass that experiences torque and forces to align with the external field (CED 12.1.B.2). If you want practice applying these ideas for the AP exam, check the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and more problems at Fiveable practice (https://library.fiveable.me/practice/ap-physics-2-revised).

Temperature changes how well a material’s atomic magnetic dipoles line up, so it changes its magnetism and permeability. For ferromagnets (iron, nickel, cobalt) higher T increases thermal agitation, breaking domain alignment—net magnetization and permeability drop, and above the Curie temperature the material becomes paramagnetic. Paramagnetic susceptibility decreases with T (Curie law: χ ∝ 1/T), so paramagnets also get weaker when heated. Diamagnetism is very weak and largely temperature-independent. In AP terms: temperature affects domain alignment (12.1.B) and therefore a material’s magnetic permeability μ (12.1.C); μ is not constant and varies with temperature, external field, and orientation. For exam prep, be ready to connect thermal disorder → reduced alignment → lower magnetization/permeability, and to name the Curie temperature for ferromagnets. For a quick topic review check the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and more unit resources/practice at the Unit 12 overview (https://library.fiveable.me/ap-physics-2-revised/unit-12) and the practice problems hub (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: because magnetic fields come from dipoles or currents, not point monopoles, so the field spreads out and gets weaker as you move away. For a bar magnet (a magnetic dipole) the external field falls off roughly as 1/r^3 with distance r from the magnet’s center (Essential Knowledge 12.1.B.1.iv). That steep falloff happens because the north and south contributions partly cancel at far distances. Different source shapes give different distance dependence: a long straight current gives B ∝ 1/r (Biot–Savart/Ampère), while a dipole (bar magnet or loop) gives B ∝ 1/r^3. Field lines always form closed loops and the magnitude decreases because the same “amount” of field is spread over a larger volume as r grows (CED Topic 12.1 concepts). For more review on this idea and how it’s tested on the AP, see the Topic 12.1 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/1-magnetic-fields/study-guide/8CQ1URzqZQqRb7qQ) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).