Faraday's law — EMF = −dΦ - dt — Hinglish notes

1.8.26 · Physics › Electromagnetism

HUM TRACK KYA KARTE HAIN?

DOT PRODUCT KYUN? Sirf woh field component jo surface ke perpendicular hai, usse hoke gujarta hai. Jo field surface ke saath sideways slide karta hai, woh kuch bhi thread nahi karta. $cos θ$ bilkul wahi perpendicular component nikaalta hai.

FIRST PRINCIPLES SE DERIVE KAISE KAREIN?

Charges par force se shuru karo (motional EMF). Ek rod lो jiska length $L$ ho, jo rails par speed $v$ se slide kar rahi ho, field $B$ page se bahar ho.

Rod mein har charge $q$ par magnetic force lagti hai $F = q v \times B$ , magnitude $q v B$ , jo use rod ke saath dhakelta hai.
Yeh force ek battery ki tarah kaam karti hai. EMF woh work hai jo rod ke across ek unit charge move karne mein hoti hai: $E = \frac{W}{q} = \frac{( q v B ) L}{q} = B v L .$
Ab ise flux se connect karo. Rod area ko rate $\frac{d A}{d t} = Lv$ se sweep karti hai. Toh $\frac{d Φ _{B}}{d t} = B \frac{d A}{d t} = B Lv = E .$

Toh "moving charges par force" wala picture aur "changing flux" wala picture same number dete hain. Faraday ki genius yeh thi ki unhone realize kiya yeh tab bhi kaam karta hai jab kuch bhi move nahi karta — sirf time-varying $B$ bhi EMF induce kar deta hai. Yeh general statement dono ko unify karta hai: $E = - \frac{d Φ _{B}}{d t} .$

MINUS SIGN KYUN (Lenz's law)? Energy conservation. Agar induced current change ko help karta, toh loop khud ko amplify karta → free infinite energy milti. Isliye induced current flux ki change ko oppose karna chahiye. Sign us opposition ko track karta hai.

Worked Examples

Steel-manned Mistakes

Flashcards

Faraday's law in words

Induced EMF us loop mein se gujarne wale magnetic flux ki negative rate of change ke barabar hoti hai.

Formula for EMF with N turns

E = - N d Φ_{B} / d t

Definition of magnetic flux

Φ_{B} = \int B \cdot d A = B A cos θ

flat loop ke liye uniform field mein.

θ

kya measure karta hai

B

aur surface normal

\overset{n}{^}

ke beech ka angle (plane nahi).

Flux ki SI unit aur uske base units

Weber (Wb) = T·m² = V·s.

Motional EMF of a rod, derive karo

Charges par force

q v B

, work per charge

= B v L

, toh

E = B v L

Flux change karne ke teen tarike

B change karna, area A change karna, ya orientation θ change karna.

Minus sign kyun hota hai

Lenz's law — induced current change ko oppose karta hai, energy conservation enforce karta hai.

Rotating coil ki peak EMF

E_{0} = N B A ω

, tab hoti hai jab loop

B

ke edge-on ho.

Kya ek fixed loop mein constant field EMF induce karta hai

Nahi — flux change nahi ho raha, toh

d Φ/ d t = 0

Recall Feynman: 12-saal ke bachche ko explain karo

Socho ek hula-hoop hai aur usme se invisible "magnetic spaghetti" guzar raha hai. Hoop mein electricity tabhi jaagti hai jab hoop mein se gujarne wale spaghetti strands ki sankhya change ho rahi ho — chahe aur daalo, kheench nikalo, ya hoop ko tilta karo. Agar strands still baithe hain toh kuch nahi hoga, chahe unki sankhya laakhon mein ho. Aur hoop grumpy hai: tum jo bhi karo, woh apni spaghetti count same rakhne ke liye pushback karta hai. Wahi pushback woh electricity hai jo tum use kar sakte ho.

Connections

Lenz's Law — minus sign ka matlab
Magnetic Flux — jis quantity ko differentiate kar rahe hain
Motional EMF — $v \times B$ ke zariye derivation
Maxwell's Equations — Faraday's law as $\nabla \times E = - \partial B / \partial t$
Electric Generators and AC — rotating-coil application
Inductance — coil ke apne changing flux se self-induced EMF