Electromagnetic forces
Calculate magnetic fields and forces on currents and charges for H2 Physics, including current balances, beam deflection and velocity selection.
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Before you begin
Electric currents make magnetic fields, and magnetic fields push on currents. The lessons start with the fields of a straight wire, a flat coil and a solenoid, then find the force on a wire in a field, which defines magnetic flux density and explains the forces between parallel wires. The same force acts on single moving charges: it bends them into circles in a magnetic field, and with an electric field added it picks out particles of one speed.
Be comfortable with: circular motion, because a charged particle in a magnetic field moves in a circle.
Learning goals
- Calculate and represent magnetic fields produced by currents.
- Sketch magnetic field lines due to currents in a long straight wire, a flat circular coil and a long solenoid.
- Analyse forces on current-carrying conductors in magnetic fields, including current balances.
- Analyse forces and paths of moving charges in uniform fields.
- Apply crossed electric and magnetic fields to velocity selection.
Syllabus statements covered
- show an understanding that a magnetic field is an example of a field of force produced either by current-carrying conductors or by permanent magnets
- sketch magnetic field lines due to currents in a long straight wire, a flat circular coil and a long solenoid
- use B = μ₀I/(2πd), B = μ₀NI/(2r) and B = μ₀nI for the magnetic flux densities of the fields due to currents in a long straight wire, a flat circular coil and a long solenoid respectively
- show an understanding that the magnetic field due to a solenoid may be influenced by the presence of a ferrous core
- show an understanding that a current-carrying conductor placed in a magnetic field might experience a force
- recall and solve problems using the equation F = BIl sin θ, with directions as interpreted by Fleming’s left-hand rule
- define magnetic flux density as the force acting per unit current per unit length on a conductor placed perpendicular to the magnetic field
- show an understanding of how the force on a current-carrying conductor can be used to measure the magnetic flux density of a magnetic field using a current balance
- explain the forces between current-carrying conductors and predict the direction of the forces
- predict the direction of the force on a charge moving in a uniform magnetic field
- recall and solve problems using the equation F = BQv sin θ
- describe and analyse deflections of beams of charged particles by uniform electric fields and uniform magnetic fields
- explain how perpendicular electric and magnetic fields can be used in velocity selection for charged particles
Lessons
Work through them in order.
Core lessons
- Magnetic fields produced by currentsSketch and calculate the magnetic fields of a straight wire, flat coil and solenoid.
- Force on a wire and current-balance measurementsUse F = BIl sin θ and Fleming's left-hand rule, define magnetic flux density and measure it with a current balance.
- Forces between parallel currentsUse each wire's field at its neighbour to explain attraction, repulsion and equal interaction forces.
- Force on a moving chargeUse F = BQv sin θ for the force on a moving charge, and explain why it changes the direction of motion but not the speed.
- Circular paths in a magnetic fieldExplain why a charged particle moves in a circle in a uniform magnetic field, and calculate the radius of its path.
- Electric beam deflection and field comparisonCalculate the deflection of a beam in a uniform electric field, and compare it with the circular path in a magnetic field.
- Velocity selection in crossed fieldsExplain how crossed electric and magnetic fields select particles of speed v = E/B.
Practise and check
Or choose
Topic reference
Quick reference
| Idea | Relation | Notes |
|---|---|---|
| long straight wire | B = μ₀I/(2π d) | circular field lines; right-hand grip rule |
| flat circular coil | B = μ₀NI/2r | at the centre |
| long solenoid | B = μ₀nI | inside; n is turns per unit length |
| force on a wire | F = BIl sin θ | Fleming’s left-hand rule |
| parallel wires | F/l = μ₀I₁I₂/(2π d) | same direction attract |
| force on a moving charge | F = BQv sin θ | reverse the direction for a negative charge |
| circular path | r = mv/BQ | velocity at right angles to a uniform field |
| velocity selector | v = E/B | electric and magnetic forces opposite |
μ₀ = 4π × 10⁻⁷ H m⁻¹
Core knowledge to remember
- A magnetic field is a field of force produced by current-carrying conductors or by permanent magnets.
- A ferrous core inside a solenoid greatly increases the strength of its field.
- Magnetic flux density is the force acting per unit current per unit length on a conductor placed perpendicular to the magnetic field.
- Parallel currents in the same direction attract; in opposite directions they repel.
- The magnetic force on a moving charge is at right angles to its velocity, so it does no work and does not change its speed.
- In crossed electric and magnetic fields, particles of speed E/B pass through undeflected, whatever their charge or mass.
Common mistakes
- Using the left hand for the grip rule, or the right hand for the force rule.
- Putting the total number of turns into B = μ₀nI.
- Using cos θ, or the angle to the wrong line, in F = BIl sin θ and F = BQv sin θ.
- Forgetting to reverse the force for a negative charge.
- Using projectile equations for motion in a magnetic field.