Key Equations

Magnetic Fields & Forces — AQA A-Level Physics

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.
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