Preview
IB DP Physics — Unit D: Fields | SL & HL | D.3 Motion in Electromagnetic Fields
📋 What You Will Learn
- Observe how charged particles behave when placed in uniform electric and magnetic fields, using real-world examples such as cathode ray tubes and particle accelerators
- Define all key quantities: electric field strength, magnetic flux density, electric force, magnetic force, and the conditions under which each acts
- Derive the equations for the force on a charged particle in an electric field and in a magnetic field from first principles
- Analyse the circular motion of a charged particle in a uniform magnetic field and derive the radius of curvature
- Apply the velocity selector principle to determine the speed of a particle when electric and magnetic forces balance
- Evaluate graph-based and figure-based problems involving particle trajectories, force directions, and the Hall effect
🌍 Real-World Context Inside a hospital's MRI machine, protons in your body are deflected by powerful magnetic fields, allowing doctors to construct detailed images of soft tissue without a single X-ray. In a particle accelerator at CERN, protons are steered around a 27-kilometre ring by superconducting magnets, reaching speeds close to the speed of light. In both cases, the same fundamental physics is at work: a moving charged particle in a magnetic field experiences a force perpendicular to its velocity, curving its path in a precise arc. Understanding how electric and magnetic fields control the motion of charged particles is not just an abstract exercise — it underpins medical imaging, television screens, mass spectrometers, and the search for the fundamental building blocks of matter.
🔍 Guiding Question How do electric and magnetic fields exert forces on charged particles, and how can these forces be combined to control the speed and trajectory of a particle with precision?
Physical Setup: A Charged Particle in a Field
Imagine releasing a small positive charge from rest between two parallel metal plates connected to a battery. The charge accelerates smoothly from the positive plate toward the negative plate, gaining kinetic energy as it moves — this is the effect of an electric field. Now imagine the same charge moving horizontally through a region where a magnetic field points into the page. Instead of speeding up or slowing down, the charge curves upward or downward, tracing a circular arc. These two scenarios — straight-line acceleration and circular deflection — are the two fundamental ways fields act on charged particles.
Notice the key difference between these two diagrams. In the electric field, the force acts along the direction of the field (parallel to the motion if the particle enters along the field direction), causing the particle to accelerate — its speed changes. In the magnetic field, the force is always perpendicular to the velocity, so the particle's speed stays constant while its direction continuously changes, producing circular motion. This distinction is central to every problem in this topic.
Core Concepts and Definitions
Before we can write any equations, we need to build a clear picture of what an electric field and a magnetic field actually are, and how each one interacts with a charged particle. An electric field exists in the space around any charged object or between charged plates. It is a vector quantity — it has both magnitude and direction. A positive test charge placed in an electric field experiences a force in the direction of the field; a negative charge experiences a force opposite to the field direction.
📖 Key Definition — Electric Field Strength The electric field strength \( E \) at a point is defined as the force per unit positive charge experienced by a small positive test charge placed at that point. It is a vector quantity, measured in newtons per coulomb (N C⁻¹) or equivalently volts per metre (V m⁻¹).
For a uniform electric field between two parallel plates separated by distance \( d \)