Electromagnetic Forces: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 17 · 9478 Topic 17 · Read time: ~11 minutes
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Key Formulas
Magnetic fields of currents
A magnetic field is a field of force produced by current-carrying conductors or permanent magnets.
Long straight wire: concentric circles, B = µ₀I/2πd. Flat circular coil: B = µ₀NI/2r at the centre. Long solenoid: uniform field inside, B = µ₀nI.
A ferrous (iron) core inside a solenoid greatly increases the flux density.
Force on a current-carrying conductor
A conductor in a magnetic field may feel a force F = BIl sin θ, where θ is the angle between the current and the field. Zero when parallel, maximum when perpendicular.
Magnetic flux density is defined as the force per unit current per unit length on a conductor placed perpendicular to the field. Unit: tesla (T).
Direction: Fleming's left-hand rule. A current balance measures B by balancing this magnetic force against a known weight.
Two parallel wires each sit in the other's field: currents in the same direction attract, opposite directions repel.
Trap: Parallel currents don't behave like charges. Same direction attracts.
Force on a moving charge
A charge moving through a magnetic field feels F = BQv sin θ, perpendicular to both v and B. For a negative charge, the force is opposite to the left-hand rule result for a positive one.
Because the force is always perpendicular to the velocity, it does no work: the speed is constant and, in a uniform field, the path is a circle with r = mv/BQ.
In a uniform electric field, by contrast, the force is constant in direction and the path is a parabola.
Trick: Magnetic field: circle, constant speed. Electric field: parabola, speed changes. That one line separates most deflection questions.
Velocity selection
In perpendicular (crossed) electric and magnetic fields, a particle passes through undeflected only if the forces balance: QE = BQv, so v = E/B, independent of charge and mass.
Faster particles are deflected by the magnetic force; slower ones by the electric force.
Worked Example
Protons (mass 1.67 × 10⁻²⁷ kg, charge 1.60 × 10⁻¹⁹ C) travel at 2.0 × 10⁵ m s⁻¹ into a uniform magnetic field of 0.10 T, perpendicular to the field.
(a) Calculate the magnetic force on a proton. [1]
F = BQv = 0.10 × 1.60 × 10⁻¹⁹ × 2.0 × 10⁵ = 3.2 × 10⁻¹⁵ N
(b) Calculate the radius of the circular path. [2]
r = mv / BQ = (1.67 × 10⁻²⁷ × 2.0 × 10⁵) ÷ (0.10 × 1.60 × 10⁻¹⁹)
= 2.1 × 10⁻² m
(c) An electric field is added perpendicular to B so that the protons pass straight through. Calculate its strength. [2]
QE = BQv, so E = Bv
= 0.10 × 2.0 × 10⁵ = 2.0 × 10⁴ V m⁻¹
Why this question is a good test of the topic: it links the magnetic force to circular motion, then shows why the velocity selector's speed doesn't depend on the particle's charge or mass.
Frequently Asked Questions
How is magnetic flux density defined?
The force per unit current per unit length on a conductor placed perpendicular to the magnetic field.
Do parallel currents attract or repel?
Currents in the same direction attract. Currents in opposite directions repel.
Why does a charged particle move in a circle in a magnetic field?
The force is always perpendicular to the velocity, so it changes only the direction, providing the centripetal force.
What is a velocity selector?
Crossed electric and magnetic fields that let through undeflected only particles with speed v = E/B.
How does an iron core affect a solenoid's field?
It greatly increases the magnetic flux density inside the solenoid.
Charged particle deflection still confusing?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.