Foundations — Coulomb's law — force, comparison with gravity

1.8.2 · D1 · Physics › Electromagnetism › Coulomb's law — force, comparison with gravity

$F=k\frac{|q_1{q}_2|}{r^2}$ padhne se pehle, tumhe jaanna chahiye ki iska har piece kya represent karta hai. Yeh page har symbol ko absolute zero se build karta hai, us order mein jo har ek ko pichle waale par lean karne deta hai. Agar koi symbol abhi yahan define nahi hua hai, toh use mat karo.

1. Charge — the symbol $q$

Picture: socho ek dot jis par ek chota label laga hai — ek $+$ dot ya ek $-$ dot. Woh label charge hai. Uske saath ka number (maano $q=3\text{C}$) kehta hai ki us dot par us flavour ka kitna hai.

Topic ko yeh kyun chahiye: Coulomb's law charges ke charges ko push karne ke baare mein hai. Agar "is dot par kitna push-stuff hai" ke liye koi symbol nahi hai, toh plug in karne ko kuch bhi nahi hai. Do flavours matter karte hain kyunki same-flavour dots repel karte hain (alag ho jaate hain) aur opposite-flavour dots attract karte hain (paas aa jaate hain) — $q$ ka sign hi decide karta hai kaun sa hoga.

2. Distance — the symbol $r$

Picture: do charged dots draw karo, phir unke centres ko connect karne wala straight line segment draw karo. Us segment ki length $r$ hai.

Topic ko yeh kyun chahiye: force weak hoti jaati hai jab charges alag hote hain. Yeh kitna weak hoti hai yeh kehne ke liye, humein "kitna door" ka ek number chahiye — woh number $r$ hai. Yeh denominator mein jaata hai, kyunki bada $r$ matlab chhoti force.

3. Force — the symbol $F$ and the arrow $\vec{F}$

Picture: ek arrow jo ek charge par se start hota hai. Arrow ki length = push kitna strong hai (woh $F$ hai, magnitude). Arrow ki direction = charge ko kis taraf dhakela jaata hai.

Topic ko yeh kyun chahiye: poora law ek cheez compute karta hai — charges ke beech ki force. $F$ (bina arrow ke) iska size hai; $\vec{F}$ (arrow ke saath) iska size plus direction hai. Tum dono se miloge, isliye ab fark seekh lo:

4. Magnitude aur bars $|\cdot |$

Picture: ek number line. $|x|$ simply $x$ zero se kitna door hai, hamesha ek positive distance.

Topic ko yeh kyun chahiye: size-only formula $F=k|q_1{q}_2|/r^2$ mein, humein "kitna strong" ke liye ek positive answer chahiye. Agar $q_1=+3$ aur $q_2=-2$ hai, toh $q_1{q}_2=-6$ hai, aur raw $-6$ se ek nonsensical negative strength milegi. Bars woh fix karte hain: $|-6|=6$. Phir hum push-ya-pull alag se signs se decide karte hain.

5. Squaring aur inverse-square shape $1/r^2$

Picture: "paint spray" picture. Ek point se har direction mein spray paint karo. $r$ doori par wahi paint ek sphere ki surface par lagayi jaati hai jiska surface area $4\pi r^2$ hai — ek area jo $r$ ke square ke saath badhta hai. Isliye paint $1/r^2$ ke hisaab se patli ho jaati hai.

Topic ko yeh kyun chahiye — aur square kyun, sirf $1/r$ kyun nahi: ek charge ka influence ek sphere ki surface par spread hota hai, aur sphere ka area $4\pi r^2$ hai. Doori double karo aur woh surface chaar guna badi ho jaati hai, isliye influence chaar guna patla ho jaata hai. Isliye law inverse-square hai, sirf inverse nahi. Yahi spreading picture exactly wahi hai jo Gauss's Law rigorous banata hai.

6. The constant $k$ (aur ${\epsilon }_0$, aur $4\pi$)

Picture: $k$ ko ek exchange rate ki tarah socho. Tum "coulombs aur metres" dete ho; $k$ tumhe wapas sahi number of newtons deta hai. Uske andar ka $4\pi$ spray picture ka sphere-ki-surface factor hai — $k=1/4\pi {\epsilon }_0$ likhne se baad ke spread-out formulas (Gauss's Law) clean aate hain.

Topic ko yeh kyun chahiye: $k$ ke bina equation galat size ki force galat units mein dega. Gravity ke constant $G=6.67\times 10^{-11}$ se compare karo: notice karo ki $k$ ka exponent bahut bada hai ($10^9$) jabki $G$ ka bahut chhota hai ($10^{-11}$). Yeh ek fact hi reason hai ki electricity colossal hai aur gravity gentle hai.

7. Charges multiply karna — product $q_1{q}_2$

Picture: ek chota sign-table.

8. Point charge — idealisation

Picture: ek fuzzy charged blob ki jagah, ek single mathematical dot jis par charge label hai — jaise figure s01 mein dots.

Topic ko yeh kyun chahiye: formula $F=k|q_1{q}_2|/r^2$ sirf point charges ke liye exact hai (ya perfect spheres ke liye, maano ki unka saara charge centre par baitha ho). Ek spread-out shape ke liye, alag-alag bits alag-alag distances par hote hain, isliye tum (Superposition Principle) add up ya integrate karte. Points se start karna arithmetic clean rakhta hai.

Foundations topic ko kaise feed karte hain

Baayein har box ek symbol hai jo ab tumhara hai. Milke yeh beech ke law mein assemble ho jaate hain, jo phir field, Gauss's law, aur gravity comparison mein grow karta hai jo tumhe parent note Coulomb's law mein milega.

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