Title: InkPhysics / Electric fields
On every note of this deck, unless a note says otherwise:
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Front: CHECK YOURSELF
Two protons sit 1.0 fm apart. Using data-booklet values, find the electric and gravitational forces between them and the ratio of the two. Why, despite this ratio, does gravity and not electricity shape galaxies?
Show a hint
Same r in both laws, so the ratio outlives it.
Back: Electric: F = Q_1Q_2/4πε_0r^2 = (8.99 × 10^9 × (1.60 × 10^−19)^2) / (1.0 × 10^−15)^2 ≈ 230 N, repulsive.
Gravitational: F = Gm^2/r^2 = (6.67 × 10^−11 × (1.67 × 10^−27)^2) / (1.0 × 10^−15)^2 ≈ 1.9 × 10^−34 N.
Ratio ≈ 1.2 × 10^36, independent of r. Galaxies still belong to gravity because bulk matter is neutral: charges cancel and electric forces screen themselves out, while masses only ever add.

Front: DEFINITION
Define: Electric field strength.
Back: The force per unit charge on a small positive test charge placed in the field: E = F/Q, in N C^−1 or V m^−1.

Front: CHECK YOURSELF
Two plates 4.0 cm apart carry a potential difference of 500 V. Find the field strength between them and the force on an electron in the gap.
Show a hint
Uniform field first, then force per charge read backwards.
Back: E = V/d = 500 / 0.040 = 1.25 × 10^4 V m^−1.
F = EQ = 1.25 × 10^4 × 1.60 × 10^−19 = 2.0 × 10^−15 N, directed towards the positive plate because the electron's charge is negative.
Tiny in newtons, enormous per kilogram: on an electron's mass this force produces an acceleration around 10^15 m s^−2.

Front: DEFINITION
Define: Electric potential.
Back: The work done per unit positive charge to move a small test charge from infinity to that point.

Front: CHECK YOURSELF
A point charge of +2.0 nC sits in air. Find the potential 0.30 m away, and the work needed to bring a +1.5 nC charge from far away to that point.
Show a hint
Radial potential first; then joules per coulomb times the coulombs.
Back: V = Q/4πε_0r = (8.99 × 10^9 × 2.0 × 10^−9) / 0.30 = 60 V.
Coming from infinity, ΔV = 60 V, so ΔW = QΔV = 1.5 × 10^−9 × 60 = 9.0 × 10^−8 J.
Positive work, supplied by whatever does the pushing: both charges are positive, so the arrival is uphill all the way.