Physics · Cheatsheet

Theme D · Fields

Chapter 1 · Field foundations

📋 Reference · always available

Newton's gravitation

F = G\frac{m_1 m_2}{r^2}

G = 6.67\times10^{-11}

N m² kg⁻².

Gravitational field strength

g = \frac{F}{m} = G\frac{M}{r^2}

Inverse-square; double

r

⇒ quarter

g

Coulomb's law

F = k\frac{q_1 q_2}{r^2}

k = 8.99\times10^{9}

N m² C⁻².

Electric field strength

E = \frac{F}{q} = k\frac{Q}{r^2}

Force per unit positive test charge.

Field lines

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

Force on moving charge

F = qvB\sin\theta

Perpendicular to both

v

and

B

(right-hand rule).

Force on current wire

F = BIL\sin\theta

Circular motion in B-field

qvB = \frac{mv^2}{r}

Charged particles follow circular paths in a uniform field;

r = \tfrac{mv}{qB}

Orbital speed

v = \sqrt{\frac{GM}{r}}

From gravity = centripetal; independent of the orbiting mass.

Field strength (uniform)

E = \frac{V}{d}

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

Work in a field

W = qV,\quad W = Fd

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

Conventional vs electron flow

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

Key SI units

F

: N ·

g

: N kg⁻¹ (= m s⁻²) ·

E

field: N C⁻¹ or V m⁻¹ ·

B

: T ·

q

: C ·

r

: m.

Common traps

Inverse-square: doubling r quarters the force; using diameter for r;

\sin\theta

F=qvB

(zero force if v ∥ B).