Lenz's law — opposing induced current: Visual walkthrough

1.8.27 · D2 · Physics › Electromagnetism › Lenz's law — opposing induced current

Hum maan lete hain tumhe kuch nahi pata. Neeche har symbol pehle earn hota hai, phir use hota hai.

Step 1 — Loop kya hota hai, aur uske through "flux" kya hai?

KYA. Sabse simple cheez se shuru karte hain: ek single closed wire — ek loop. Paas mein ek bar magnet rakha hai. Magnet apne N (north) end se invisible arrows sprays karta hai jise magnetic field lines kehte hain, aur wapas apne S (south) end mein. Un arrows ki strength aur direction kisi point par $B$ likhi jaati hai (upar ka chota arrow matlab "is quantity ki ek direction hai").

KYUN. Pehle change ki baat karne se, humein woh cheez chahiye jo change hoti hai. Woh cheez hai magnetic flux, likha jaata hai $Φ_{B}$ . Flux sirf count karta hai kitne field arrows loop ko pierce karte hain.

PICTURE. Figure mein, loop ek flat ring hai. Red arrows magnet ki field lines hain jo usse pierce kar rahi hain. Ring ke through jyada arrows = jyada flux.

Step 2 — Magnet ko hilao: ab flux change karta hai

KYA. Magnet ka N-pole loop ki taraf kisi speed se slide karo. Jaise yeh paas aata hai, ring ke paas uska field stronger hota jaata hai, toh aur arrows loop ko pierce karte hain. Arrow count $Φ_{B}$ badhta hai.

KYUN. Lenz's law poori tarah change ke baare mein hai. Ek frozen magnet kuch nahi karta. Sirf changing flux loop ko life mein stirr karta hai. "Count kitni tezi se change ho raha hai" measure karne ke liye humein ek tool chahiye: rate of change, likha jaata hai $\frac{d Φ _{B}}{d t}$ .

PICTURE. Do snapshots: magnet door (ring ke through kam arrows) aur magnet paas (bahut arrows). Frames ke beech arrow-count mein jump hi change hai.

Step 3 — Maano loop change ki madad karta (forbidden universe)

KYA. Bas ek pal ke liye imagine karo, ek loop jo magnet ki himmat badhata hai: jaise N-pole paas aata hai, loop apna nazdiki face ek S-pole bana leta hai (opposite poles attract) aur magnet ko aur tezi se andar kheenchta hai.

KYUN. Hum yeh fantasy test karte hain isko impossible prove karne ke liye. Tez magnet → flux aur tezi se badhta hai → loop aur zyada kheenchta hai → magnet forever accelerate karta hai → koi push kiye bina unlimited electrical energy baahir aati hai. Yeh ek aise machine hai jo kuch se energy banaata hai, jo kisi experiment ne kabhi allow nahi kiya.

PICTURE. Ek runaway spiral: speed arrow badhta hai, pull arrow badhta hai, ek doosre ko feed karte hain. Yeh red mein cross out hai — yeh universe exist nahi karta.

Step 4 — Loop ko oppose karna hi hoga: nazdiki face N ban jaata hai

KYA. Reality iska ulta behavior choose karti hai. Jaise N-pole paas aata hai (flux rising), loop apna nazdiki face N-pole bana leta hai. Like poles repel karte hain, toh loop magnet ko peechhe dhakelta hai.

KYUN. Yahi ek aisi choice hai jo energy conserve karti hai: magnet ko andar push karte rehne ke liye, tumhe repulsion ke against work karna padta hai, aur woh work loop ki electrical energy ban jaata hai — kuch free nahi. Ring ke andar loop ka field magnet ki taraf baahir point karta hai, badh rahe incoming field ka part cancel karta hai — yeh increase se ladta hai.

PICTURE. Loop par red "N" label magnet ki taraf; do N's ek doosre ko ghoor rahe hain; ek red repulsion arrow magnet ko peechhe push kar raha hai.

Step 5 — Right hand se current direction padho

KYA. Hum jaante hain loop ka field ring se baahir magnet ki taraf point karna chahiye. Ab humein chahiye ki actual current kis direction mein run kare toh woh field bane.

KYUN. Current aur uska field Right-hand rule se locked together hain: apna right thumb desired field ke saath point karo, aur tumhari curled fingers current ki circular direction dikhati hain. Hum yeh rule use karte hain (aur guesswork nahi) kyunki yeh current loop aur uske field ke beech fixed geometric link hai.

PICTURE. Ek right hand: thumb ring se baahir magnet ki taraf, fingers counterclockwise curl karti hain (magnet ki side se dekha jaaye). Woh curl hi current hai.

Recall Ulta case khud check karo

Magnet ko door kheecho: flux girta hai, toh loop isko rakhe rakhna chahta hai → nazdiki face S ban jaata hai (attract, "wapas aao!") → field andar magnet ki taraf point karta hai → right hand doosri taraf curl karo → current clockwise run karta hai. Har sign flip hua kyunki change flip hua. Yeh parent note mein Example 2 ko mirror karta hai.

Step 6 — Isko number do: sliding rod

KYA. Magnet ki jagah ek clean quantitative case lo. Ek straight rod length $L$ speed $v$ se do rails par slide karta hai, sab ek uniform field $B$ mein nahaaye hue jo page mein andar point karta hai. Rod aur rails ek aisa rectangle enclose karte hain jiska width $x$ rod ke move karne par badhta hai.

KYUN. Yahan har symbol measurable hai, toh hum verify kar sakte hain ki energy books balance karti hain — minus sign ka sabse gehra reason. Motional EMF and sliding rod dekho.

PICTURE. Rod (red) right slide kar raha hai; ✕ symbols field ko page mein andar mark karte hain; shaded enclosed area wide hoti jaati hai; drag arrow rod par backward point karta hai.

Step 7 — Degenerate cases (kabhi uncovered mat chhodna)

KYA & KYUN, teen edge cases:

Rod at rest ( $v = 0$ ). Toh $\frac{d Φ _{B}}{d t} = B L \cdot 0 = 0$ : koi change nahi, koi EMF nahi, koi current nahi, koi drag nahi. Standing flux, chahe kitna bhi bada ho, kuch nahi karta.
Field loop ke parallel ( $θ = 9 0^{\circ}$ ). Toh $Φ_{B} = B A cos 9 0^{\circ} = 0$ hamesha. Chahe kitna bhi move karo — zero arrows pierce karte hain, toh zero induced current. Akela motion kaafi nahi; flux actually change hona chahiye.
Constant flux, moving parts. Agar ek loop uniform field ke through translate kare bina enclosed area ya angle change kiye, arrow-count fixed rehta hai → $\frac{d Φ _{B}}{d t} = 0$ → kuch nahi. Lenz change par react karta hai, kabhi sirf presence ya sirf motion par nahi.

PICTURE. Teen mini-panels: (a) still rod, koi drag nahi; (b) loop edge-on arrows ke paas, zero pierce; (c) loop uniform field mein glide karta hua, count unchanged. Har ek par red "0" stamped.

Ek-picture summary

Is page par sab kuch ek single chain mein: flux change karo → nature oppose karti hai → current opposing way mein run karta hai → tum energy pay karte ho → books balance hoti hain.

Recall Poore walkthrough ki Feynman retelling

Ek wire loop ek lazy guard dog hai. Uske paas magnet hilao aur kuch nahi hota — dog tabhi jaagta hai jab magnet hilta hai (woh flux changing hai, sirf wahan baithe rehna nahi). Agar magnet charge kare andar, dog ek matching north naak growl karta hai aur isko wapas dhakelta hai; agar magnet bhaage, dog ek south naak ugaata hai aur isko wapas kheenchta hai — hamesha cheezein exactly waise rakhne ki koshish karta hai jaise woh thi. Kyun dog friendly nahi ho sakta aur magnet ko andar pull kar sakta hai? Kyunki woh aur tezi aur tezi spin karega aur tumhe forever free energy dega, jo universe bilkul refuse karta hai. Toh dog zaroor resist karta hai, aur resist karne ke liye woh tumhari pushing arm ki energy heat ke roop mein burn karta hai. Woh "tum push karo, yeh heat hota hai, kuch free nahi" hi $ε = - \frac{d Φ _{B}}{d t}$ mein minus sign hai.

Quick self-check

Ek loop ke through flux rise ho raha hai — induced field

B

ke saath point karega ya against?

B

ke against, arrow-count neeche rakhne ke liye.

Sliding rod ke liye, kyun

\frac{d Φ _{B}}{d t} = B Lv

Kyunki

Φ_{B} = B Lx

aur sirf

x

change hota hai, rate

v

par.

Agar rod ruk jaaye, toh induced current kya hoga?

Zero — flux mein koi change nahi, toh koi EMF nahi.

P = F v = I^{2} R

kya prove karta hai?

Mechanical power jo tum supply karte ho exactly heat dissipated ke barabar hai — energy conserve hoti hai.

Connections

Parent: Lenz's law — yeh page isko pictures mein derive karta hai.
Faraday's law of induction — woh EMF magnitude provide karta hai jisme hamaara sign attach hota hai.
Magnetic flux — woh $Φ_{B} = B A cos θ$ jo hum count karte hain.
Right-hand rule — field direction ko current direction mein convert karta hai (Step 5).
Motional EMF and sliding rod — Step 6 mein quantitative case.
Eddy currents and magnetic braking — bulk metal ke andar wahi drag.
Conservation of energy — woh reason jisse forbidden universe (Step 3) forbidden hai.
Self-inductance and back-EMF — Lenz apne current ko oppose karne wale circuit par apply hua.