Further Mechanics, Fields and Particles

WPH14Unit 47 topics · 25 questions

Key equations

The relationships this unit leans on most. Check your formulae or data booklet for which ones the exam gives you.

4.4Capacitors4 questions

$E_k = \dfrac{p^2}{2m}$

kinetic energy from momentum (useful in collisions)

$\omega = \dfrac{\Delta\theta}{\Delta t} = \dfrac{2\pi}{T}$: angular velocity
$v = \omega r$: linear speed on a circle of radius $r$
$a = \dfrac{v^2}{r} = r\omega^2$
$F = \dfrac{mv^2}{r}$: resultant (centripetal) force needed

$E = \dfrac{F}{Q}$: electric field strength: force per unit charge
$F = \dfrac{Q_1Q_2}{4\pi\varepsilon_0 r^2}$: Coulomb's law between point charges
$E = \dfrac{Q}{4\pi\varepsilon_0 r^2}$
$E = \dfrac{V}{d}$: uniform field between parallel plates
$V = \dfrac{Q}{4\pi\varepsilon_0 r}$: potential of a point charge

$C = \dfrac{Q}{V}$: capacitance
$W = \tfrac{1}{2}QV = \tfrac{1}{2}CV^2$: energy stored: area under a $Q$ – $V$ graph
$Q = Q_0e^{-t/RC}$: discharge through a resistor; $RC$ is the time constant

$F = BIl\sin\theta$: force on a current-carrying wire in a field $B$
$F = Bqv\sin\theta$: force on a moving charge
$r = \dfrac{p}{BQ}$: radius of a charged particle's circle in a uniform field

$\Phi = BA\cos\theta$: magnetic flux through an area
$\varepsilon = -\dfrac{d(N\Phi)}{dt}$: Faraday's and Lenz's laws: induced e.m.f.

2

centripetal acceleration, towards the centre

2

field of a point charge

2

R

C