Foundations — Self-inductance L, mutual inductance M

1.8.28 · D1 · Physics › Electromagnetism › Self-inductance L, mutual inductance M

Is page pe assume kiya gaya hai ki tumhe kuch nahi pata. $L=N\Phi /I$ padhne se pehle tumhe pata hona chahiye ki $N$, $\Phi$, aur $I$ mein se har ek ka kya matlab hai, har ek kaisa picture draw karta hai, aur topic ko uski zaroorat kyun hai. Hum unhe ek-ek karke build karte hain, har ek pichle pe rest karta hua.

0. Electric current $I$ — woh flow jisse hum shuru karte hain

Ise picture karo: pipe mein paani imagine karo. Current $I$ woh hai — har second kitne litre ek cross-line se guzarte hain — pipe mein kitna paani hai woh nahi, balki kitni tezi se flow kar raha hai.

Topic ko iski zaroorat kyun hai: current hi yahan sab kuch ki cause hai. Koi current nahi → koi magnetic field nahi → koi flux nahi → koi inductance nahi. Baad mein poori kahani is baare mein hai ki jab $I$ change hota hai to kya hota hai, isliye pehle ise naam dena zaroori hai.

1. Magnetic field $B$ — jo ek current apne aas-paas create karta hai

Ise picture karo: apna right hand ek wire ke aas-paas wrap karo apna thumb current ki direction mein pointing rakh ke — tumhari curled fingers dikhati hain ki $\vec{B}$ kis taraf wire ke around circle karti hai. Ek coil ke andar, woh saare circles milke ek strong field banate hain jo coil ki axis ke seedha neeche run karta hai.

Topic ko iski zaroorat kyun hai: $B$ woh invisible middle-man hai. Current apne aap ko aur apne neighbour ko sirf usi field ke through "feel" kar sakta hai jo woh banata hai. Dekho Ampère's law ki hum $I$ se $B$ kaise compute karte hain.

2. Area vector $\vec{A}$ — us loop ko describe karna jisme se field guzarti hai

Ise picture karo: ek hula-hoop pakdo. Area uske andar ki disc hai; area-arrow $\vec{A}$ ek skewer hai jo seedha middle se ghusa hua hai, hoop ke right angles pe.

Topic ko iski zaroorat kyun hai: yeh poochhne ke liye ki "loop se kitna field guzarta hai" humhe pata hona chahiye ki loop kis taraf face kar raha hai. Skewer ke along field puri tarah se guzarta hai; face ke across slide karta hua field bilkul nahi guzarta.

3. Magnetic flux $\Phi$ — loop se kitna field guzarta hai

Ise picture karo: $\vec{B}$ ko girte hue baarish ki tarah socho aur loop ko ek ring ki tarah jo use pakadne ke liye upar rakhi gayi ho. Agar ring baarish ka seedha samna kare, toh woh sabse zyada pakadti hai (full flux). Use tilt karo aur woh kam pakadti hai; edge-on rakho aur woh kuch nahi pakadti.

$\cos$ kyun aur kuch aur kyun nahi? $\cos \theta$ exactly woh fraction hai arrow $\vec{B}$ ka jo along skewer $\vec{A}$ lie karta hai. Yeh jawab deta hai "field ka kitna hissa genuinely andar ja raha hai, versus across slide kar raha hai?" Ek solenoid ke andar field seedha axis ke along run karta hai aur loop use face karta hai, isliye $\theta =0$ aur hume simply $\Phi =BA$ milta hai — isliye parent note cosine drop kar deta hai. Dekho Magnetic flux.

Topic ko iski zaroorat kyun hai: flux woh star quantity hai. Inductance define hi flux-per-amp ke roop mein hoti hai, isliye $L$ likhe bina $\Phi$ ke hum likhh hi nahi sakte.

4. Turns $N$ aur flux linkage $N\Phi$ — har loop ko count karna

Ise picture karo: ek hi skewer pe $N$ identical rings stack karo. Har ring same flux $\Phi$ pakadti hai; coil as a whole unhe "feel" karti hai, isliye uska total linkage $N$ times zyada hota hai.

Topic ko iski zaroorat kyun hai: Faraday's law total linkage $N\Phi$ ke respond karta hai, ek loop ke nahi. Yahi famous $L\propto N^2$ ki source hai: zyada turns ka matlab zyada field banana (ek factor of $N$) aur zyada turns use link karne ke liye (doosra factor of $N$).

5. Rate of change $\frac{dI}{dt}$ — "kitni tezi se change ho raha hai?" ka tool

Ise picture karo: yeh $X$ ka time ke against graph ki steepness hai. Flat line → zero. Steep uphill → big positive. Downhill → negative.

Yahi tool kyun aur sirf $I$ kyun nahi? Kyunki Faraday's law change ki parwah karta hai, amount ki nahi. Ek bahut bada steady current ek bahut bada steady flux banata hai — lekin kuch change nahi hota, isliye kuch induce nahi hota. Sirf $dI/dt$ (ya $d\Phi /dt$) hi ek coil ko fight back karwa sakta hai. Exactly isliye working formula $\epsilon =-LdI/dt$ hai aur nahi $\epsilon =-LI$.

6. Induced EMF $\epsilon$ aur minus sign — woh fight-back voltage

Minus sign kyun? Yeh Lenz's law hai: induced EMF hamesha aise point karta hai jisse us change ko oppose kare jisne ise cause kiya. Agar flux badh raha hai, EMF use shrink karne ki koshish karta hai; agar ghatt raha hai, EMF use prop up karne ki koshish karta hai. Nature sudden change se resist karti hai — isliye ek coil "stubborn" act karti hai.

Topic ko iski zaroorat kyun hai: $\epsilon$ woh observable consequence hai. $L$ aur $M$ sirf woh constants hain jo changing current ko is measurable voltage mein badal dete hain. Dekho Faraday's law of induction.

7. Sab kuch milao — $L$ aur $M$ kahan se aate hain

Ab har symbol earn ho gaya hai, definitions saaf padhti hain:

Time mein differentiate karo (geometry fixed hai, isliye $L$ aur $M$ constants hain) aur Faraday use karo: ${\epsilon }_{\text{self}}=-L\frac{dI}{dt},{\epsilon }_2=-M\frac{d{I}_1}{dt}$

Yahi parent topic ka poora engine hai.

Prerequisite map

Ise top-down paadho: current field banata hai, field aur area milke flux banate hain, flux times turns linkage banata hai, linkage per amp inductance hai, aur inductance times rate of change (Lenz ke minus sign ke saath) woh EMF hai jo tum actually measure karte ho.

Chain lock karne ke liye ek worked micro-example

Equipment checklist

Khud test karo — right side cover karo aur reveal karne se pehle zor se jawab do.