D.3
Motion in Electromagnetic Fields
Force on charges and currents in electric and magnetic fields, circular motion of charged particles, velocity selectors, and forces between current-carrying wires.
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D.3 Motion in Electromagnetic Fields
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Key Concepts, Motion in Electromagnetic Fields
Force on a Charged Particle in a Magnetic Field
A charged particle moving through a magnetic field experiences a force given by F = qvB sinθ, where q is the charge, v is the speed, B is the magnetic flux density and θ is the angle between the velocity and the field. The force is always perpendicular to both the velocity and the field, so it never does work on the particle and never changes its speed, only its direction. The direction of the force is found using the left-hand rule (for conventional current or positive charges): point the first finger in the field direction, second finger in the velocity direction, and the thumb points in the direction of the force. For a negative charge, the force is reversed.
Circular Motion of Charged Particles
Because the magnetic force is always perpendicular to velocity, a charged particle moving at right angles to a uniform magnetic field follows a circular path. The magnetic force provides the centripetal force: qvB = mv²/r, which rearranges to r = mv/qB. The radius increases with momentum (mv) and decreases with charge and field strength. The period of circular motion T = 2πm/qB is independent of speed, which is the principle behind the cyclotron. The charge-to-mass ratio q/m can be found from r = mv/qB if v is known, or from the period T = 2πm/qB if the field and period are measured.
Motion in a Uniform Electric Field
A charged particle in a uniform electric field experiences a constant force F = qE, where E = V/d for parallel plates. This produces uniform acceleration along the field direction, exactly analogous to projectile motion under gravity. If the particle enters the field perpendicular to the field lines (as in a deflection tube), its path is parabolic: it accelerates in the field direction while continuing at constant speed perpendicular to it. This is the basis of cathode ray tube deflection and particle accelerator steering.
Velocity Selector (Crossed Fields)
When a uniform electric field and a uniform magnetic field are perpendicular to each other and to the initial particle velocity, particles of a specific speed travel straight through without deflection. The electric force qE and magnetic force qvB act in opposite directions. For no deflection: qE = qvB, giving v = E/B. Particles moving faster are deflected by the magnetic force; slower particles are deflected by the electric force. Only particles with exactly v = E/B pass straight through. This device selects particles of a specific speed regardless of their charge or mass.
Force on a Current-Carrying Conductor
A current-carrying conductor in a magnetic field experiences a force F = BIL sinθ, where I is the current, L is the length of conductor in the field and θ is the angle between the current direction and the field. This is the motor effect: the force is perpendicular to both the current and the field. The direction is found using the left-hand rule. Maximum force occurs when the current is perpendicular to the field. If the current is parallel to the field, there is no force.
Force Between Parallel Current-Carrying Wires
Two parallel wires carrying currents each produce a magnetic field that acts on the other wire. The force per unit length between them is F/L = μ₀I₁I₂/(2πd), where μ₀ = 4π × 10⁻⁷ T m A⁻¹ is the permeability of free space, I₁ and I₂ are the currents and d is the separation. Wires carrying currents in the same direction attract each other. Wires carrying currents in opposite directions repel. This interaction was historically used to define the ampere.
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Frequently Asked Questions, IB Physics Motion in Electromagnetic Fields
What is Motion in Electromagnetic Fields in IB Physics? ↓
Force on charges and currents in electric and magnetic fields, circular motion of charged particles, velocity selectors, and forces between current-carrying wires. This topic is part of Theme D (Fields) in the current IB Physics syllabus.
Is Motion in Electromagnetic Fields SL or HL in IB Physics? ↓
Motion in Electromagnetic Fields is covered by both SL and HL students in the current IB Physics syllabus. HL students study additional depth and extension content beyond the SL core.
What equations do I need for IB Physics Motion in Electromagnetic Fields? ↓
The key equations for Motion in Electromagnetic Fields are covered in the concept tutorial above. For a structured set of notes with all equations, conditions and worked examples, the GradePod Exam Pack includes a revision note template for every topic.
What are common exam mistakes in IB Physics Motion in Electromagnetic Fields? ↓
Common mistakes are covered in detail in the exam technique video above. The GradePod Exam Pack also includes exam-style questions with mark schemes so you can see exactly how marks are awarded and where students typically drop them.
How do I revise Motion in Electromagnetic Fields for the IB Physics exam? ↓
Follow the GradePod three-step method. First, watch the concept tutorial and tick off each learning objective on the checklist above as you go. Second, watch the exam technique video to see how IB-style questions are answered under exam conditions. Third, use the Exam Pack to practise independently with knowledge questions, exam questions and mark schemes. That's it. It works. I promise.