Displacement current — Maxwell's addition to Ampere's law: Foundations

1.8.32 · D1 · Physics › Electromagnetism › Displacement current — Maxwell's addition to Ampere's law

Is page par koi assumption nahi hai. parent topic mein use hone wala har symbol yahan ground up se build kiya gaya hai. Ise upar se neeche padho — har idea ek aisa brick hai jis par agla idea tikta hai.

1. Field kya hota hai?

Figure — Displacement current — Maxwell's addition to Ampere's law

Electric field $E$ aisa hi ek arrows ka map hai. Har point par yeh batata hai ki kaunsi direction mein aur kitni force se wahan rakha gaya ek tiny positive charge push hoga.

Letter ke upar ka chota arrow, $E$ , matlab hai "yeh ek vector hai" — iske paas sirf size nahi balki direction bhi hai.
Iska size (arrow kitna lamba hai) bina arrow ke $E$ likhte hain.

Magnetic field $B$ bhi yahi idea hai — arrows ka ek map — lekin yeh arrows magnets aur moving charges ko feel hote hain, aur yeh kisi source se door point karne ki jagah loops banate hain.

2. Charge, aur current asal mein kya hota hai

$\frac{d Q}{d t}$ ko padho: " $Q$ abhi kitni tezi se badh raha hai?" Kisi quantity ke aage $d$ ka matlab hai usme ek tiny change, aur ek cheez doosre ke upar $\frac{d ( yeh )}{d ( woh )}$ rate hai — yeh cheez woh ki per unit kitni change hoti hai. (Yeh derivative hai; hum ise isliye use karte hain kyunki "rate of change" wahi sawaal hai jo hum baar baar poochte hain.)

Definition Do tareh ke current jinhe hum name denge

Kyunki yeh topic real flowing charge ko changing field ke current jaisi acting se compare karta hai, hum inhe abhi alag names dete hain taaki baad mein koi symbol surprise na kare:

Conduction current $I_{c}$ — wire mein actual charge flow karna, $I_{c} = \frac{d Q}{d t}$ . Yeh upar wala ordinary current hai; subscript $c$ sirf kehta hai "conduction (charge actually moves)."
Displacement current $I_{d}$ — ek changing electric field ka magnetic effect, §5 mein define hoga jab flux milega. Koi charge move nahi karta; subscript $d$ kehta hai "displacement."

Jab baad mein hum poochhein "kitna current ek surface ko pierce karta hai?" — jawaab conduction, displacement, ya dono ho sakta hai. Hum jo bhi matra kisi chosen surface se guzarti hai use enclosed current kehte hain, $I_{e n c}$ likhte hain (subscript $e n c$ = "loop ke andar"). To $I_{e n c}$ ek role hai jo current play karta hai, jabki $I_{c}$ aur $I_{d}$ kaunsa type hai yeh batate hain.

3. Area as a vector, aur dot product

"Flux" se pehle do choti ideas chahiye.

Dot product kyun, plain multiplication kyun nahi? Kyunki humein $E$ ka woh part chahiye jo actually surface ke through poking kar raha ho. Agar $E$ surface ke along slide karta hai (angle $9 0^{\circ}$ ), kuch bhi through nahi jaata — aur wakai $cos 9 0^{\circ} = 0$ product ko khatam kar deta hai. Dot product woh exact tool hai jo jawaab deta hai "kitna seedha through jaata hai?"

4. Electric flux $Φ_{E}$ — show ka star

Ek bumpy surface ya non-uniform field ke liye, hum surface ko tiny patches $d A$ mein kaat dete hain, har ek $E \cdot d A$ lete hain, aur sab add kar dete hain. Woh "infinitely many tiny pieces ko surface par add karna" integral sign se likha jaata hai: $Φ_{E} = \int E \cdot d A$

5. Constant $ε_{0}$ aur displacement current $I_{d}$

Displacement current build karne se pehle humein ek "exchange-rate" constant chahiye.

Ab hum §2 mein promise ki gayi definition complete kar sakte hain:

6. Loop ke around line integral $\oint B \cdot d l$

$\oint B \cdot d l$

Har step par hum $B \cdot d l$ lete hain — magnetic field kitna hamare step ke along point karta hai — aur loop ke around sab add kar dete hain.

Hume ek doosra "exchange-rate" constant bhi chahiye is circulation ko current se connect karne ke liye.

7. Orientation: right-hand rule jo loop aur surface ko link karta hai

Ek hidden agreement hai jo humein fix karni hai, warna signs galat ho jaate hain. Loop integral $\oint B \cdot d l$ ko loop ke around travel ki direction chahiye, aur flux $Φ_{E} = \int E \cdot d A$ ko area vector $d A$ ki direction chahiye. Yeh do choices independent nahi hain — inhe right-hand rule manna padta hai.

8. Constants saath mein, aur surface charge density $σ$

Hum $ε_{0}$ (§5) aur $μ_{0}$ (§6) alag alag mile. Saath mein yeh ek famous secret chupaate hain.

Gauss's Law mein use hota hai is clean result ke liye ki capacitor plates ke beech $E = σ / ε_{0}$ — ek uniform field, gap mein har jagah same arrow-length.

Yeh bricks topic kaise build karte hain

Equipment checklist

Khud test karo — sirf jawaab dene ke baad reveal karo.

E

ke upar wale chote arrow ka kya matlab hai?

Yeh ek vector ko mark karta hai — ek aisi quantity jisme size aur direction dono hain.

Ek phrase mein, field kya hota hai?

Ek rule jo space ke har point par ek arrow (value + direction) deta hai.

Current ko charge ki rate of change ke roop mein likho.

I = \frac{d Q}{d t}

(coulombs per second = amperes).

\frac{d ( something )}{d t}

kya poochh raha hai?

"Woh cheez abhi kitni tezi se change ho rahi hai?" — rate of change.

Conduction current

I_{c}

kya hai?

Wire mein actual charge flow karna,

I_{c} = d Q / d t

I_{e n c}

mein subscript

e n c

ka kya matlab hai, aur yeh

I_{c}

aur

I_{d}

se kaise relate karta hai?

"Loop ke andar enclosed" — chosen surface se guzarne wala total current,

I_{e n c} = I_{c} + I_{d}

;

I_{c}

I_{d}

kind batate hain,

I_{e n c}

role batata hai.

Area vector

A

kaunsi direction mein point karta hai?

Surface ke perpendicular, jiski length area ke barabar hoti hai.

Flux ke liye plain multiplication ki jagah dot product

E \cdot A

kyun use karte hain?

Yeh sirf

E

ka woh part rakhta hai jo surface ke through point kar raha ho; surface ke along slide karne wala field (

9 0^{\circ}

) kuch contribute nahi karta kyunki

cos 9 0^{\circ} = 0

Electric flux

Φ_{E}

physically kya count karta hai?

Kitne electric-field arrows ek given surface ko pierce karte hain.

Displacement current

I_{d}

define karo.

I_{d} = ε_{0} \frac{d Φ _{E}}{d t}

— changing electric flux ka magnetic effect (koi charge move nahi karta).

\oint

par circle kya batata hai?

Sum ek closed loop ke bilkul around, wapas start tak chalta hai.

\oint B \cdot d l

kya measure karta hai?

Magnetic field loop ke around kitna circulate (swirl) karta hai.

Loop direction aur surface normal

d A

kaise related hain?

Right-hand rule se: right-hand fingers walk ke along curl karo, thumb

d A

deta hai.

Yeh rule displacement-current term ke liye kyun matter karta hai?

Yeh

ε_{0} d Φ_{E} / d t

ka sign fix karta hai; loop reverse karne se dono sides saath flip hoti hain, law consistent rehta hai.

ε_{0}

kya hai, uski value aur unit kya hai?

Permittivity of free space,

\approx 8.85 \times 1 0^{- 12} F m^{- 1}

— charge ko electric field se link karta hai.

μ_{0}

kya hai, uski value aur unit kya hai?

Permeability of free space,

4 π \times 1 0^{- 7} H m^{- 1}

(

= N A^{- 2}

) — current ko magnetic field se link karta hai.

Dono currents ke naam ke saath poora Ampère–Maxwell law likho.

\oint B \cdot d l = μ_{0} (I_{c} + I_{d}) = μ_{0} I_{c} + μ_{0} ε_{0} d Φ_{E} / d t

1/ μ_{0} ε_{0}

kaunsi famous quantity hai, aur yeh speed kyun hai?

Speed of light

c

; units

F m^{- 1} \cdot H m^{- 1}

s^{2} m^{- 2}

milta hai, jiski reciprocal root

m s^{- 1}

hai.

Capacitor plates ke beech

σ

ke terms mein

E

kya hai?

E = σ / ε_{0}

(Gauss's Law se).

Connections

Parent topic (Hinglish) — jahan yeh foundations use hoti hain
Ampère's Law — loop integral $\oint B \cdot d l$ use karta hai
Gauss's Law — $σ$ se plates ke beech field deta hai
Faraday's Law of Induction — flux par built, mirror twin
Maxwell's Equations — destination
Parallel Plate Capacitor — canonical picture
Electromagnetic Waves — payoff
Speed of Light — constant $1/ μ_{0} ε_{0}$