12.2 Magnetism and Moving Charges

A current-carrying wire feels a magnetic force because the wire’s moving charges (electrons) interact with an external magnetic field. The magnitude for a straight wire of length L carrying current I in a uniform field B is F = I L B sinθ, where θ is the angle between the wire’s current direction and B (special cases: 0 → no force, 90° → max force). The force direction is perpendicular to both I and B, given by the right-hand rule (point your thumb along I, fingers along B; your palm shows the force direction on positive charges—for electron flow reverse it). This is just the bulk form of the Lorentz force on individual charges (FB = q v B sinθ). On the AP exam you’ll need to identify magnitudes for 0°, 90°, 180° and use right-hand rule reasoning. For more review and practice problems on Topic 12.2, see the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and unit resources (https://library.fiveable.me/ap-physics-2-revised/unit-12).

A current-carrying wire feels a force in a magnetic field because the wire’s moving charges (the electrons) are acted on by the magnetic part of the Lorentz force. Each charge q moving at velocity v in a field B feels FB = q v B sinθ, where θ is the angle between v and B, and the force is perpendicular to both v and B (use the right-hand rule). In a wire, many charges moving along the wire give a net force proportional to current: F = I L B sinθ (a direct consequence of summing qv forces over charges). That’s why a straight wire perpendicular to B (θ = 90°) feels the largest force, and a wire parallel to B (θ = 0° or 180°) feels none—consistent with the CED’s sinθ dependence and right-hand-rule direction. For AP review, see the Topic 12.2 study guide on Fiveable (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of the magnetic force as a 3D cross product—it’s always perpendicular to both the velocity/current and the magnetic field. Step-by-step right-hand rule (for AP Physics 2, use either qv×B or IL×B): 1. Pick the proper vector: for a single positive charge use velocity v; for a current-carrying wire use current I (same direction as positive charge flow). 2. Point your index finger in the direction of v (or current I). 3. Point your middle finger in the direction of the magnetic field B (keep it perpendicular to the index finger). 4. Your thumb (now perpendicular to both) points in the direction of the magnetic force F. 5. If the charge is negative, the force is opposite your thumb. For a wire, the same rule gives the force on the wire segment (use F = I L × B in magnitude form F = I L B sinθ; for charges use FB = q v B sinθ). 6. On the AP exam, quantitative work with angles is limited to 0°, 90°, and 180°—remember sin0=0, sin90=1, sin180=0. For a focused review of Topic 12.2 and practice problems, check the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and the unit page (https://library.fiveable.me/ap-physics-2-revised/unit-12).

They're related but different things. Magnetic field produced by a moving charge: a moving charge creates a B-field in the space around it (Biot–Savart idea). At a point the field direction is perpendicular to both the charge's velocity and the position vector to that point (use the right-hand rule). Its magnitude depends on the charge's speed and the distance to the point, and is largest when velocity and position vector are perpendicular (CED 12.2.A). Force on a moving charge in a magnetic field: this is what the field does to a charge already in that field—given by the Lorentz force FB = q v B sinθ (CED 12.2.B). The force is perpendicular to both v and B (right-hand rule), so it changes the direction of velocity (circular or helical motion when perpendicular) but does no work when purely perpendicular. Quick exam tip: know the difference between “field produced by” (source) and “force on” (interaction with an existing B). For more review, see the Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Use the sinθ factor exactly: sin0° = 0, sin90° = 1, sin180° = 0. So for F = qvB sinθ: - θ = 0° (v parallel to B): sin0 = 0 → F = 0. No magnetic force; charge moves along field lines. - θ = 90° (v perpendicular to B): sin90 = 1 → F = qvB (maximum magnitude). Direction is perpendicular to both v and B (use the right-hand rule; for a negative charge reverse the direction). - θ = 180° (v anti-parallel to B): sin180 = 0 → F = 0. No magnetic force again. Remember AP’s boundary: you only need to do quantitative work for 0°, 90°, and 180°; other angles are treated qualitatively (sinθ dependence). For a current-carrying wire use the analogous F = ILB sinθ. For more review and practice on Topic 12.2, see the Fiveable study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and lots of practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

The Hall effect is just charge carriers getting pushed sideways by a magnetic field and making a voltage across the conductor. When current (moving charges) flows through a metal or semiconductor and a magnetic field has a component perpendicular to that motion, the magnetic part of the Lorentz force (q v × B) deflects charges to one side. That buildup of charge creates a transverse electric field. At equilibrium the electric force (qE) balances the magnetic force (qvB), so charges stop piling up and you get a steady Hall voltage across the sample. The Hall voltage is proportional to B and the current and depends on carrier density and sign (so it tells you whether carriers are positive or negative). Use the right-hand rule/Lorentz-force idea to predict direction. This is exactly what the CED calls the Hall effect (12.2.B.4). For a quick review, see the Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

If a straight wire carrying current I sits in a magnetic field B, the magnetic force on a length L is FB = I L B sinθ—so the angle θ between the current direction (velocity of charges) and B matters. Two key AP cases (boundary statement): - Parallel (θ = 0° or 180°): sinθ = 0 so FB = 0. No magnetic force; the wire feels no sideways push. - Perpendicular (θ = 90°): sinθ = 1 so FB = I L B (max). The force’s direction is perpendicular to both I and B; use the right-hand rule (point fingers along I, curl toward B, thumb shows FB on positive charges). Qualitatively, intermediate angles give FB proportional to sinθ; direction always ⟂ to I and B (Lorentz-force idea). For quick AP review of this topic and worked examples, see the Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

You need this because magnetic forces on current-carrying wires are the physics behind a lot of real devices and the kinds of problems you’ll see on the AP exam. Practically: motors and generators use F = I L × B (the Lorentz-force idea) to turn electrical energy into motion or vice versa; loudspeakers move a wire coil in a magnetic field to make sound; magnetic brakes and maglev trains use induced currents and magnetic forces for controlled motion; and the Hall effect lets sensors measure magnetic fields or current. On the CED level, understanding direction with the right-hand rule and how force depends on current, wire length, and B (and angles) lets you predict motion and design systems (12.2.B, 12.2.A keywords: Lorentz force, right-hand rule, Hall effect). Unit 12 is worth ~12–15% of the MC section, so practice these setups and free-response translations. Review the Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and try problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of a current-carrying wire as lots of moving charges. The magnetic force on each charge follows the Lorentz rule F = q v × B (CED 12.2.B). For a macroscopic straight segment of wire, those tiny forces add up to FB = I L × B in vector form and |FB| = I L B sinθ (CED 12.2.B.2.i). To get direction use the right-hand rule for current: point your thumb along the conventional current (direction positive charges move), point your fingers along B, and your palm (or the direction your fingers curl into when you close them) shows the force on the wire (perpendicular to both I and B)—this is the same perpendicular rule in the CED. If the moving charges are electrons (negative), the actual force is opposite the thumb direction. On the AP exam you can state directions qualitatively and use angles 0°, 90°, 180° for magnitudes (CED boundary). For a quick review, see the Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and extra practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of the wire as lots of moving charges. Each charge q moving with velocity v in a magnetic field B feels a Lorentz force F = q v × B (magnitude qvB sinθ) that’s perpendicular to both v and B. In a current-carrying wire those charges move together; the forces on all charges add up to a net force on the wire. For a straight segment of length L carrying current I, that net force is F = I L × B (or F = ILB sinθ for magnitude), where θ is the angle between the current direction and B. Use the right-hand rule to get direction: thumb = current, fingers = B, palm gives force on a positive-charge current. This is exactly what AP Topic 12.2 covers (moving charges → magnetic field; magnetic force on moving charges and on currents). For a quick review, see the Topic 12.2 study guide on Fiveable (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

When a current flows in a conductor placed in a magnetic field that has a component perpendicular to the charge motion, the magnetic (Lorentz) force qv × B pushes charge carriers sideways. That transverse deflection makes charges pile up on one side and leave the opposite side more negative, creating a perpendicular electric field and a measurable potential difference—the Hall voltage. The buildup continues until the electric force qE balances the magnetic force qvB (for the 90° case), so E = vB. For a conductor of width w, V_H = E w = v B w (using the charge carriers’ drift speed v; sign depends on whether carriers are positive or negative). This is a qualitative application of the CED idea that magnetic fields exert perpendicular forces on moving charges (F_B = q v B sinθ) and explains why a Hall voltage appears when B has a component perpendicular to the current (see the Topic 12.2 study guide on Fiveable for more review: https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5). For extra practice, try problems at https://library.fiveable.me/practice/ap-physics-2-revised.

Because the magnetic force on a moving charge comes from the Lorentz force law F = q(v × B), its direction is given by the cross product v × B—that math makes F perpendicular to both v and B. The magnitude is q v B sinθ, so the force is zero when v is parallel or antiparallel to B (θ = 0° or 180°) and maximal when v ⟂ B (θ = 90°). Physically that perpendicularity means the magnetic force changes the charge’s direction but not its speed, so charges curve into circular or helical paths (cyclotron motion, gyroradius/Larmor radius). Use the right-hand rule to pick the sign/direction for positive charges (flip for negative). This is exactly what the CED calls out (12.2.B.2.i–ii) and is a core idea you should be able to describe qualitatively on the AP exam. For a focused review, see the Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and try practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

When a charged particle moves through both E and B fields it feels two independent forces: the electric force F_E = qE and the magnetic (Lorentz) force F_B = q v × B with magnitude q v B sinθ (CED 12.2.B.2). Those add vectorially to give the net force F = qE + q v × B (CED 12.2.B.3). So outcomes depend on directions: if v is parallel to B then F_B = 0 and only E accelerates the particle; if v ⟂ B and E = 0 the particle moves in a circle; if both fields exist you can get curved, helical, or straight motion. A useful special case: choose E so qE = −q v × B and the net force is zero—that’s a velocity selector. For AP review, focus on the sinθ dependence, right-hand rule for direction, and the independence of the two forces (see the Topic 12.2 study guide on Fiveable: https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5). For extra practice, use the unit practice set (https://library.fiveable.me/practice/ap-physics-2-revised).

Use the magnetic force law for a current: F = I L × B. The direction is perpendicular to both the current (conventional direction of positive charge flow) and the magnetic field—so you use the right-hand rule. Two easy right-hand methods: - Two-vector rule (qv×B style): Point your fingers in the direction of the current (I), rotate your palm/fingers toward the magnetic field B, and your thumb points in the direction of the magnetic force F. - Three-finger rule (mutual perpendiculars): Hold your right hand so your index finger points along I, your middle finger points along B, and your thumb then points along F. Quick checks: if I is parallel or anti-parallel to B, the force is zero; if I is perpendicular to B, the force is maximal. On the AP, you’ll be expected to state direction qualitatively and treat magnitudes quantitatively mainly for 0°, 90°, 180° (see CED Topic 12.2.B). For extra practice, see the Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and lots of practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

If you put a current-carrying wire near a magnet you’ll see the wire feel a sideways push—perpendicular to both the current and the magnet’s B-field. Qualitatively: the magnetic field exerts a force on the moving charges in the wire (Lorentz force). Magnitude (useful for lab reasoning): F = I L B sinθ, so the force grows with current I, the length L in the field, and B; it’s largest at θ = 90° and zero if the wire runs parallel to the field (θ = 0° or 180°). Direction: use the right-hand rule (thumb = conventional current, fingers = B, palm points in force direction on positive charges). If the wire is free to move it will deflect; reversing the current flips the force direction. For AP-style review and quick practice problems, check Topic 12.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-4/2-magnetism-and-moving-charges/study-guide/EquvYgnfwi2ptpX5) and the Unit 12 overview (https://library.fiveable.me/ap-physics-2-revised/unit-12).