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Magnetism
Eduqas A Level Physics — Revision Notes
Component 2 & 3: Magnetic Fields and Electromagnetic Induction
Magnetic Fields and Flux Density
A magnetic field exerts forces on moving charges and current-carrying conductors. The field is described by the magnetic flux density B, measured in Tesla (T). Magnetic field lines run from North to South outside a magnet, and the field is stronger where lines are closer together.
Magnetic Flux Density
B is defined via the force on a current-carrying conductor:
F = BIL sin θ
where L is the length of conductor in the field, I is the current, and θ is the angle between the current direction and the field. Maximum force when θ = 90◦^ (current perpendicular to field); zero force when the current is parallel to the field. 1 T is the field that produces a force of 1 N on a 1 m conductor carrying 1 A perpendicular to the field.
Force Direction: Fleming’s Left-Hand Rule Point the First finger in the direction of the Field, the seCond finger in the direction of the (conventional) Current, and the thuMb gives the direction of the Motion (force). This rule only applies when the current has a component perpendicular to the field.
Force on a Moving Charge
A single charge Q moving at velocity v through a magnetic field B at angle θ experiences a force: F = BQv sin θ This force is always perpendicular to the velocity, so it does no work and cannot change the speed — only the direction. If v is perpendicular to B, the charge moves in a circle.
Circular Motion of Charged Particles
Setting the magnetic force equal to the centripetal force:
BQv =
mv^2 r
=⇒ r =
mv BQ
A larger momentum means a larger radius. A stronger field means a tighter circle. This principle underpins mass spectrometers and particle accelerators (cyclotrons).
The Motor Effect and Electric Motors
When a current-carrying conductor sits in a magnetic field, the magnetic force on the moving charges is transmitted to the conductor itself — this is the motor effect. A rectangular coil carrying current in a uniform field experiences a torque (turning force), which is how electric motors work.
The torque on a coil of N turns, area A, carrying current I at angle θ to the field:
τ = BIN A cos θ
Maximum torque when the coil plane is parallel to B (θ = 0); zero torque when the coil is perpendicular to B.
Electromagnetic Induction
Moving a conductor through a magnetic field, or changing the magnetic flux through a coil, generates an EMF. This is electromagnetic induction.
Magnetic Flux Magnetic flux Φ is defined as: Φ = BA cos θ where A is the area of the coil and θ is the angle between B and the normal to the coil. Units: Weber (Wb), where 1 Wb = 1 T m^2. Flux linkage for a coil of N turns: N Φ = N BA cos θ.
Faraday’s Law
The magnitude of the induced EMF equals the rate of change of flux linkage:
E = −
d(N Φ) dt
= −N
dΦ dt
The minus sign encodes Lenz’s Law. For a conductor of length L moving at speed v perpendicular to a field B: E = BLv
Lenz’s Law
Lenz’s Law The induced EMF (and hence the induced current) always acts in a direction such that it opposes the change in flux that caused it. This is simply conservation of energy in disguise: if the induced current helped the motion, energy would be created from nothing.
To determine the direction of induced current: use the right-hand rule or imagine the induced current creating a magnet that repels the incoming flux change.
B and the conductor. Lenz’s Law questions: state that the induced current opposes the cause and explain what that means physically. For transformers: if voltage steps up, current steps down by the same factor (ideal transformer).
