Theme D · Fields

$G = 6.67\times10^{-11}$ N m² kg⁻².

Inverse-square; double $r$ ⇒ quarter $g$.

$k = 8.99\times10^{9}$ N m² C⁻².

Force per unit positive test charge.

Leave +, enter −; closer lines = stronger field. Gravity always attractive.

Perpendicular to both $v$ and $B$ (right-hand rule).

Charged particles follow circular paths in a uniform field; $r = \tfrac{mv}{qB}$.

From gravity = centripetal; independent of the orbiting mass.

Between parallel plates; units V m⁻¹ (= N C⁻¹).

Energy gained by charge q across p.d. V (J).

Magnetic force directions use conventional current (+). Electrons (−) experience the opposite-sense force.

$F$: N · $g$: N kg⁻¹ (= m s⁻²) · $E$ field: N C⁻¹ or V m⁻¹ · $B$: T · $q$: C · $r$: m.

Inverse-square: doubling r quarters the force; using diameter for r; $\sin\theta$ on $F=qvB$ (zero force if v ∥ B).

Webers (Wb); max when field ⟂ surface.

EMF = rate of change of flux linkage.

Induced current opposes the change that made it — energy conservation.

A stationary magnet in a coil induces nothing; flux must be *changing*.

Rod length $L$ moving at $v$ across field $B$.

Step up/down AC voltage via turns ratio.

Step UP voltage ⇒ step DOWN current (power conserved if 100% efficient).

Units Wb (= T m²); the bigger this changes per second, the bigger the EMF.

Current in a field feels a force; reverse current OR field to reverse it.

$\Phi$: Wb · $B$: T · $A$: m² · $\varepsilon, V$: V · $N$: (no unit) · $\tfrac{d\Phi}{dt}$: Wb s⁻¹ = V.

Dropping the minus sign / forgetting Lenz; a steady (unchanging) flux gives ZERO EMF; using $\theta$ from the surface instead of the normal in $\Phi=BA\cos\theta$.