Magnetic Fields & Forces

Flux density, forces on wires and charges, circular orbits, and the current balance practical.

Spec Points Covered
  • Define magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³.The strength of a magnetic field. The force per unit length per unit currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). on a currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).-carrying conductor perpendicular to the field. Measured in teslaThe SI unit of magnetic flux density. One tesla is the flux density when a force of 1 N acts on a 1 m conductor carrying 1 A perpendicular to the field. (T). and state the definition of the teslaThe SI unit of magnetic flux density. One tesla is the flux density when a force of 1 N acts on a 1 m conductor carrying 1 A perpendicular to the field..
  • Apply $F = BIL \sin \theta$ to calculate the force on a currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).-carrying conductor.
  • Use Fleming's left-hand rule to determine force, field, and current directions.
  • Apply $F = BQv \sin \theta$ to calculate the force on a moving charged particle.
  • Derive and apply $r = mv / BQ$ for the circular path of a charged particle.
  • Describe and analyse the required practical for measuring magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³.The strength of a magnetic field. The force per unit length per unit current on a current-carrying conductor perpendicular to the field. Measured in teslaThe SI unit of magnetic flux density. One tesla is the flux density when a force of 1 N acts on a 1 m conductor carrying 1 A perpendicular to the field. (T)..
Notes
01 A magnetic field is defined by the force it exerts Magnetic field 3.7.5.1 → 02 Magnetic flux density tells you how strong the field is Magnetic flux density 3.7.5.1 → 03 Flux lines show direction and strength at the same time 3.7.5.1 → 04 Force on a current-carrying conductor: F = BIL sin θ $F = BIL \sin \theta$ 3.7.5.1 → 05 Fleming's left-hand rule finds the force direction Fleming's left-hand rule 3.7.5.1 → 06 Force on a moving charge: F = BQv sin θ $F = BQv \sin \theta$ 3.7.5.2 → 07 Charged particles follow circular paths in uniform B-fields Circular path of a charged particle 3.7.5.2 → 08 Cyclotrons use circular orbits to accelerate particles Cyclotron 3.7.5.2 → 09 Required practical: measuring B with a current balance 3.7.5.1 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
Force on a current-carrying conductor
$$F = BIL \sin \theta$$
  • Where:
    • $F$ = force (N)
    • $B$ = magnetic flux density (T)
    • $I$ = current (A)
    • $L$ = length of conductor in field (m)
    • $θ$ = angle between conductor and field (°)
Maximum when θ = 90° (F = BIL). Zero when θ = 0°.
B from the current balance practical
$$B = \frac{g \times \text{gradient}}{L}$$
  • Where:
    • $B$ = magnetic flux density (T)
    • $g$ = gravitational field strength (9.81 m s⁻²)
    • $gradient$ = gradient of m vs I graph (kg A⁻¹)
    • $L$ = length of wire in field (m)
From mg = BIL rearranged as m = (BL/g)I. Gradient of m-I graph gives BL/g.
Force on a moving charge
$$F = BQv \sin \theta$$
  • Where:
    • $F$ = force (N)
    • $B$ = magnetic flux density (T)
    • $Q$ = charge (C)
    • $v$ = speed (m s⁻¹)
    • $θ$ = angle between velocity and field (°)
Same physics as F = BIL but for a single particle.
Radius of circular path
$$r = \frac{mv}{BQ}$$
  • Where:
    • $r$ = radius of path (m)
    • $m$ = mass of particle (kg)
    • $v$ = speed (m s⁻¹)
    • $B$ = magnetic flux density (T)
    • $Q$ = charge (C)
Derived by equating centripetal force (mv²/r) to magnetic force (BQv). Must be able to derive.
Centripetal force (for derivation)
$$F = \frac{mv^2}{r}$$
  • Where:
    • $F$ = centripetal force (N)
    • $m$ = mass (kg)
    • $v$ = speed (m s⁻¹)
    • $r$ = radius (m)
From the Circular Motion section of the data sheet. Used to derive r = mv/BQ.
Q Retrieval Practice All 14 Questions →
Q1. Define a magnetic field.
A region of space in which a magnetic pole will experience a force.
Q2. State two sources of a magnetic field.
A moving electric charge, and a permanent magnet.
Q3. Define magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³.The strength of a magnetic field. The force per unit length per unit current on a current-carrying conductor perpendicular to the field. Measured in tesla (T). B and state its unit.
  • The number of magnetic fluxThe product of magnetic flux density and the area perpendicular to the field. Measured in weberThe SI unit of magnetic flux. One weber is the flux through an area of 1 m² when the magnetic flux density is 1 T perpendicular to the area. (Wb). lines passing through a region of space per unit area.
  • Measured in teslas (T).
Q4. Define one tesla.
The flux density that causes a force of 1 N on a 1 m wire carrying a current of 1 A at right angles to the flux.
Q5. State the equation for the force on a current-carrying conductor in a magnetic field.
F = BIL sin θ, where F = force (N), B = flux density (T), I = current (A), L = length of conductor in the field (m), θ = angle between conductor and field.