Foundations — Applications — sphere, cylinder, infinite plane

1.8.7 · D1 · Physics › Electromagnetism › Applications — sphere, cylinder, infinite plane

Yeh page parent note Applications — sphere, cylinder, infinite plane mein use hone wale har symbol ko zero se build karta hai. Agar parent ne koi symbol bina explain kiye likha hai, toh tum use pehle yahan explained paoge.

1. Charge $Q$ aur $q$ — har cheez ka source

Yeh topic ko kyun chahiye: parent mein har formula "kitna charge hai?" se shuru hota hai — ek sphere $Q$ hold karta hai, ek wire charge per length hold karti hai, ek sheet charge per area hold karti hai. Charge ke bina compute karne ke liye koi field hi nahi.

Picture mein arrows hi electric field hain, jise hum aage milenge.

2. Electric field $\vec{E}$ — space mein bhar diye gaye arrows

Yeh topic ko kyun chahiye: $\vec{E}$ woh unknown hai jise hum har case mein solve karte hain (sphere, cylinder, plane).

3. Radial direction, aur distance symbols $r$, $s$, $R$

Parent teen alag distance letters use karta hai. Yeh interchangeable nahi hain — inhe mix karna #1 galti hai.

Yeh topic ko kyun chahiye: poori trick yeh hai ki symmetry $\vec{E}$ ko radial hone par majboor karti hai aur sirf $r$ par depend karne par (ya sirf $s$ par), toh woh matching surface par constant hoti hai.

4. Charge densities $\rho$, $\lambda$, $\sigma$ — charge phail gaya

Real charge rarely ek single dot hota hai; yeh ek length, ek area, ya ek volume par spread hota hai. "Density" matlab hai "us cheez ke unit per kitna charge."

5. Area vector $d\vec{A}$ — ek patch jo point karta hai

Yeh topic ko kyun chahiye: yeh measure karne ke liye ki kitne field arrows ek patch ko pierce karte hain, hum field arrow $\vec{E}$ ko patch ke apne arrow $d\vec{A}$ se compare karte hain. Woh comparison dot product hai, next.

6. Dot product $\vec{E}\cdot d\vec{A}$ — "kitna andar se pierce hota hai"

Is concept ko apne topic ke roop mein dekhne ke liye Electric Flux dekho.

7. Closed-surface integral $\oint \vec{E}\cdot d\vec{A}$ — bag se bahar total flux

8. Enclosed charge $Q_{enc}$ aur constant ${\epsilon }_0$

Pieces ko ek saath rakhne par woh master tool milta hai jo parent shuru karta hai: ${\oint }_S\vec{E}\cdot d\vec{A}=\frac{Q_{enc}}{{\epsilon }_0}$

9. Symmetry — woh ingredient jo ise solvable banata hai

10. Conductor facts jo tumhe import karne chahiye

Yeh topic ko kyun chahiye: isliye "ek conducting shell ke andar, $E=0$" ($Q_{enc}=0$) aur isliye ek conductor ki surface $E=\sigma /{\epsilon }_0$ deti hai (sirf ek taraf field) instead of isolated-sheet wali $\sigma /2{\epsilon }_0$. Yeh aage wale Parallel Plate Capacitor aur Electric Potential chapters ko bhi underlie karta hai.

Prerequisite map

Equipment checklist

Khud ko test karo — sirf jawab dene ke baad reveal karo.