Superposition principle for forces: Question bank — Hinglish deep dive

1.8.3 · D5 · Physics › Electromagnetism › Superposition principle for forces

Yahan har jagah ek hi law test ho raha hai: net force, Coulomb's Law se mile independent pair forces ka vector sum hai, jisme har force ko aisa compute karo jaise woh charge akela ho.

True ya False — justify karo

Recall

Agar kisi ek source ka charge $q_{i}$ double kar do, toh woh $q_{0}$ par jo force lagata hai woh double ho jaati hai aur koi bhi doosra pair force nahi badalta. ::: True — Coulomb's law har source charge mein linear hai, aur superposition kehta hai ki baaki terms untouched rehti hain, isliye sirf woh ek term scale hoti hai.

Recall

Do interacting charges ke beech ek bada charge rakhne se unke beech ki force kam ho jaati hai. ::: False — vacuum mein har pair force independent hoti hai; beech wala charge sirf apna khud ka force term add karta hai har ek par, woh kisi existing pairwise force ko kabhi screen ya kamzor nahi karta.

Recall

Superposition, Coulomb ke inverse-square law ka logical consequence hai. ::: False — inverse-square har pair force ko fix karta hai, lekin linearity (ki forces bina kisi cross-term ke simply add hoti hain) ek alag experimental fact hai jo Coulomb's law ko respect karna hota hai.

Recall

Agar $q_{0}$ par do source forces magnitude mein equal aur direction mein opposite hain, toh net force zero hai, chahe dono sources abhi bhi act kar rahe hon. ::: True — vectors cancel ho jaate hain, lekin har charge apni poori independent force laga raha hai; "zero net" ka matlab "koi force nahi" nahi hai.

Recall

Superposition electric field par bhi utni hi tarah laagu hoti hai jitni force par. ::: True — kyunki $F = q_{0} E$ aur $q_{0}$ ek common factor hai, isliye $E = \sum E_{i}$ bhi usi identical vector-sum rule ko follow karta hai (dekho Electric Field).

Recall

Continuous charge (ek charged rod) ke liye superposition laagu nahi hoti kyunki add karne ke liye alag-alag charges hote hi nahi. ::: False — tum rod ko infinitesimal pieces $d q$ mein tod dete ho, har ek ek point source hai, aur sum ek integral ban jaata hai $F = \int d F$ (dekho Continuous Charge Distributions).

Recall

Kai charges se electric potential energy ko bhi vector addition ki zaroorat hoti hai. ::: False — potential (aur potential energy) ek scalar hai, isliye tum bas apne signs ke saath numbers add karte ho — koi direction nahi, koi components nahi (dekho Electric Potential).

Error dhundho

Recall

"Ek charge par $3 N$ aur $4 N$ ki do forces act kar rahi hain, toh net force $7 N$ hai." ::: Yeh tabhi true hai jab woh collinear aur same direction mein hon. Agar perpendicular hain, toh net $3^{2} + 4^{2} = 5 N$ hai; answer angle par depend karta hai, jo bataya hi nahi gaya.

Recall

" $q_{0}$ par force ke liye unit vector $\overset{r}{^}_{0 i}$ , $q_{0}$ se source $q_{i}$ ki taraf point karta hai." ::: Ulta hai. $q_{0}$ par force ke liye, $\overset{r}{^}_{0 i}$ , source $q_{i}$ se $q_{0}$ ki taraf point karta hai, taaki like charges (positive product) automatically $q_{0}$ ko door dhakele.

Recall

" $q_{0}$ negative hai, isliye mein final net force ke aage haath se minus sign lagata hoon." ::: Haath se sign mat lagao — $q_{0}$ ka sign andar har Coulomb term mein $q_{0} q_{i}$ product ke zariye hai. Isse do baar fix karne par double-counting hoti hai aur direction galat flip ho jaati hai.

Recall

"Net force $(F_{x}, F_{y}) = (- 2, - 3)$ nikli, toh angle $arctan (3/2) \approx 5 6^{\circ}$ hai $+ x$ axis ke upar." ::: Dono components negative hain, isliye vector third quadrant mein hai; sahi direction $18 0^{\circ} + 5 6^{\circ} \approx 23 6^{\circ}$ hai. Akelay $arctan$ se quadrant pata nahi chalta — component signs check karo (dekho Vector Addition and Resolution).

Recall

"Mein ne har pair force ki magnitude nikaali, unhe add karke $∣ F ∣$ paaya, phir un magnitudes se angle nikala." ::: Sirf magnitudes se direction recover nahi ho sakti. Tumhe har force ko $x$ aur $y$ components mein resolve karna hoga, components ko sum karna hoga, tab magnitude aur angle banana hoga.

Why wale questions

Recall

Coulomb's law ke vector form mein denominator mein $r^{3}$ kyun hai jabki scalar form mein $r^{2}$ hai? ::: Direction ko $\overset{r}{^} = (r_{0} - r_{i}) /∣ r_{0} - r_{i} ∣$ likhne se denominator mein $r$ ki ek extra power aa jaati hai; numerator $(r_{0} - r_{i})$ phir direction carry karta hai.

Recall

Superposition, principle mein, false kyun ho sakti thi? ::: Agar forces "saturate" hoti (ek charge sirf itni hi total force feel kar sakta) ya agar charges ek doosre ko nonlinearly screen karte, toh simple additive rule toot jaata — nature bas ittefaqan high precision tak linear hai.

Recall

$q_{0}$ ka sign jaanne se attraction vs repulsion ke liye haath se bane arrows kyun hata sakte hain? ::: Product $q_{0} q_{i}$ like signs ke liye positive hota hai ( $q_{0}$ ko $\overset{r}{^}_{0 i}$ ke along bahar dhakelta hai) aur unlike signs ke liye negative (andar kheenchta hai), isliye algebra khud direction set kar deta hai.

Recall

Ek charge configuration ki potential energy ko superpose karna force se aasaan kyun hai? ::: Energy ek scalar hai — tum signed numbers ko bina direction ke add karte ho — jabki force ko components mein poori vector bookkeeping chahiye.

Edge cases

Recall

Do identical positive charges ek line par $q_{0}$ ke dono taraf symmetrically hain. Net force kya hai? ::: Zero — dono forces magnitude mein equal aur exactly opposite hain, isliye cancel ho jaati hain; $q_{0}$ us line par unstable equilibrium mein hai.

Recall

Separation $r \to 0$ hone par ek pair force ka kya hota hai? ::: Yeh infinity tak diverge ho jaati hai ( $1/ r^{2} \to \infty$ ); point-charge model contact par toot jaata hai, isliye yeh ek idealization limit hai, real infinite force nahi.

Recall

Jab ek source charge infinitely door chala jaata hai ( $r \to \infty$ ), toh net force mein uska contribution kya hota hai? ::: Yeh $1/ r^{2}$ ki tarah zero ho jaata hai, isliye door ke charges sum se bahar ho jaate hain — lekin woh kabhi negative correction contribute nahi karte, bas fade hote hain.

Recall

Teen equal positive charges ek equilateral triangle ke vertices par hain. Kya unme se kisi ek par net force zero hai? ::: Nahi — dono forces magnitude mein equal hain lekin $6 0^{\circ}$ alag hain, isliye woh ek nonzero vector mein add hoti hain jo triangle ke center se radially bahar point karta hai.

Recall

Agar saare charges (source aur target) negative hain, toh kya superposition ka form badal jaata hai? ::: Nahi — vector-sum formula identical hai; signs sirf har product $q_{0} q_{i}$ ke through enter hote hain, jo in like charges ke liye positive hai, mutual repulsion deta hai.

Recall

Ek charge $q_{0}$ ek uniformly charged ring ke exact center par baitha hai. Ring usmein kya net force lagaati hai? ::: Zero — symmetry se har $d q$ element ka ek diametrically opposite partner hota hai jiska force use cancel kar deta hai, isliye integrated superposition vanish ho jaata hai.

Connections

Superposition principle for forces — woh parent jisko yeh bank drill karta hai.
Coulomb's Law — single-pair force jis par har item build karta hai.
Vector Addition and Resolution — quadrant traps ke peeche component machinery.
Electric Field — same superposition, force per unit charge.
Continuous Charge Distributions — sum-becomes-integral edge case.
Electric Potential — scalar-superposition contrast.
Principle of Linear Superposition (Waves) — doosre domain mein same additive idea.