Coulomb's law — force, comparison with gravity

1.8.2 · Physics › Electromagnetism

WHAT is Coulomb's Law?

Charge ki unit coulomb (C) hai. Ek coulomb bahut bada hota hai — ek electron pe sirf $e = 1.6 \times 1 0^{- 19} C$ charge hota hai.

WHY does it have this shape? (Derivation-from-scratch reasoning)

Hum Coulomb's law ko kisi deeper cheez se "derive" nahi karte (ye ek experimental law hai), lekin hum argue kar sakte hain ki har piece aisa kyun hona chahiye.

Vector form (HOW to use it correctly with direction)

Newton's third law se, $F_{12} = - F_{21}$ .

Comparison with Gravity

Feature	Coulomb (electric)	Newton (gravity)
Source	charge $q$	mass $m$
Constant	$k = 8.99 \times 1 0^{9}$	$G = 6.67 \times 1 0^{- 11}$
Distance law	$1/ r^{2}$	$1/ r^{2}$
Sign	$\pm$ → attract ya repel	always attract
Strength	bahut zyada	bahut kam
Shield ho sakti hai?	haan	nahi

Kitni zyada strong? (ek derivation jo yaad rakhne layak hai)

Do electrons ke liye, electric repulsion aur gravitational attraction ka ratio lo: $\frac{F _{e}}{F _{g}} = \frac{k e ^{2} / r ^{2}}{G m _{e}^{2} / r ^{2}} = \frac{k e ^{2}}{G m _{e}^{2}}$

Numbers daalo ( $e = 1.6 \times 1 0^{- 19}$ , $m_{e} = 9.11 \times 1 0^{- 31}$ ): $\frac{F _{e}}{F _{g}} \approx 4.2 \times 1 0^{42}$

Common Mistakes (Steel-manned)

Recall Feynman: 12-saal ke bacche ko explain karo

Socho do magnets, lekin electricity ke liye. Har charged cheez ki ek invisible reach hoti hai. Ye reach door jaane par bahut tezi se weak ho jaati hai — do guna door jao aur ye chaar guna weak ho jaati hai (sirf do nahi). Plus-aur-plus door dhakelte hain, plus-aur-minus ek saath snap ho jaate hain. Gravity weight ke saath usi tarah kaam karti hai charge ki jagah, lekin gravity sirf pull karti hai aur inanely weak hai — do tiny specks ke beech electricity unki gravity se trillions-of-trillions times zyada strong hai. Hum gravity feel karte hain sirf isliye kyunki bade objects mein equal plus aur minus hote hain, to unki electricity cancel ho jaati hai.

Active-Recall Flashcards

Do point charges ke liye Coulomb's law kya kehta hai?

F = k ∣ q_{1} q_{2} ∣/ r^{2}

, unhe milane wali line ke along; like charges repel, unlike attract.

k = 1/4 π ε_{0}

ki value?

\approx 8.99 \times 1 0^{9} N\cdotm^{2} / C^{2}

ε_{0}

ki value aur matlab?

8.85 \times 1 0^{- 12} C^{2} / N\cdotm^{2}

, permittivity of free space.

Agar distance double ho, Coulomb force kaise change hoti hai?

One quarter ho jaati hai (inverse-square).

Do electrons ke

F_{e} / F_{g}

ratio mein

r

kyun cancel hota hai?

Dono forces

\propto 1/ r^{2}

hain, isliye distance divide out ho jaati hai.

Do electrons ke beech electric aur gravitational force ka approx ratio?

Lagbhag

4 \times 1 0^{42}

Coulomb aur gravity mein sign ka main difference?

Charge ± ho sakta hai isliye electric force attract ya repel karta hai; gravity hamesha attract karti hai.

Signed charges vs magnitudes kab use karte hain?

Vector form mein signed charges (sign direction set karta hai); scalar magnitude formula mein magnitudes.

Gravity large scales pe dominate kyun karti hai, chahe weak ho?

Bade bodies electrically neutral hoti hain (+ aur − cancel ho jaate hain), sirf gravity bachti hai.

k = 1/4 π ε_{0}

mein

4 π

kyun?

Ye influence ke sphere ke area

4 π r^{2}

pe phailne se aata hai; Gauss's law ko clean banata hai.

Connections

Electric Field — force per unit charge, Coulomb's law ko generalise karta hai.
Gauss's Law — kyun $1/ r^{2}$ closed surfaces se flux deta hai.
Newton's Law of Gravitation — same $1/ r^{2}$ skeleton.
Superposition Principle — many charges ki Coulomb forces ko vectors ki tarah add karna.
Electric Potential Energy — Coulomb force ko distance ke upar integrate karna.