Class 12 Physics Chapter 2: NCERT Solutions

Electrostatic Potential and Capacitance

Is chapter mein hum electrostatic force aur electric field ko aur gehrai se samajhte hain—basically, hum yahan pehle se seekhe hue concepts ko twist karte hain. Electric potential, potential difference, equipotential surfaces, aur capacitors—ye sab kuch yahan padhne ko milta hai. Aur honestly, ye sab ek dusre se jude hue hain. Ek ko pakad lo, baaki khud aa jayenge. Dekho, ye concepts sirf yahan ke liye nahi hain; aage ke chapters mein bhi kaam aayenge—jaise current electricity ya electromagnetic induction, wahan inki zaroorat padegi hi. Waise, ye topic samajhna thoda tricky ho sakta hai. Especially jab equipotential surfaces ka diagram banate ho, toh dimaag ghoom jata hai—lekin agar basics clear ho, toh baaki sab easy lagta hai.

Key Topics Covered:

• Okay, here's a rewrite that keeps the heading context in mind. --- Electric potential and the energy it stores. That's the heart of it. We're talking about the potential energy a charge has because of where it sits in an electric field. How that translates into the electric potential—the work needed to move a unit charge around. They're two sides of the same coin, really. You can't have one without the other. So, yeah, that's the core of what's covered here.
• Potential energy tied to a single point charge? Yeah, that's a thing. And it doesn't stop there—dipoles bring their own twist to the story. So we're looking at both, side by side.
• Capacitance and capacitors—that's the real meat here. We dig into how capacitance actually works, why it matters, and what makes capacitors tick. From the basic physics to the practical side, it's all on the table. No fluff, just the core stuff you need to wrap your head around.
• Capacitors wired together—that’s the gist. You string them up in series, you line them up in parallel, or you mix both in one messy, glorious circuit. Each setup changes the total capacitance in its own way, and the math shifts depending on which route you take. Series drops the overall value, parallel stacks it higher. Get the combo right and you’ve got the exact behavior your circuit needs.
• The energy that a capacitor holds when it’s fully charged—that’s the heart of this one. We’re talking about the stored charge, the voltage across the plates, and how that all adds up to real, usable power. It’s not just theory; it’s the whole game.

Links for Chapter-wise Download NCERT Solution for Class 12 भौतिकी विज्ञानI in hindi Language

Here we have provided NCERT Solution for Class 12 भौतिकी विज्ञानI in hindi Language, Just select the chapters below to get solution of the same:

स्थिर वैधुत विभव तथा धारिता

विद्युत धारा

गतिमान आवेश और चुंबकत्व

चुंबकत्व एवं द्रव्य

वैधुत चुंबकीय प्रेरण

प्रत्यावर्ती धारा

वैधुत चुंबकीय तरंग

Detailed NCERT Solutions for Chapter 2

Is chapter ke solutions mein hum har sawal ko ek-ek karke todenge, step by step, taaki aapke andar fundamental concepts pakke ho jaayein. Lekin shuruaat kahan se karein? Sabse pehle, electric potential ki definition ko theek se samajh lena zaroori hai—kyunki agar yeh base clear nahi hai, toh aage ka poora safar uljhan bhar jayega. Toh chalo, isi se shuru karte hain.

Electric Potential: Basic Concept

Electric potential ka matlab samjho—woh kaam jo ek unit positive charge ko infinity se utha kar kisi specific point tak le aane mein lagta hai. Bas itna hi. Iska SI unit Volt hota hai, aur formula hai V = kQ/r. Isse hum kisi bhi charge distribution ka effect kisi bhi point par nikal sakte hain—chahe woh ek charge ho ya poori system.

Potential due to Different Charge Configurations

• A single point charge sets up the simplest possible field. You just take the charge, divide by the distance, and slap on that constant. That's it. V = (1/4πε₀) * (q/r). No geometry to fight with, no weird cancellations. Just one charge sitting there, and the potential drops off cleanly as you pull away. It's the baseline. Everything else, every other configuration, is just a variation on this one.
• So here’s the thing about an electric dipole—it’s not the same everywhere you look. Stick with me, because this is where the geometry really kicks in. If you’re sitting on the axial line, the line that runs straight through both charges, you get a potential that’s given by V = (1/4πε₀) * (p/r²). That’s the full deal, no shortcuts. But flip over to the equatorial line, the one that cuts perpendicular right through the middle, and boom—the potential drops to exactly zero. Not small, not negligible, but precisely zero. Kind of wild when you think about it: same dipole, two completely different answers, just based on which direction you’re looking from.
• A system of charges? Simple math. The net potential is just the algebraic sum—add them all up. V = V1 + V2 + V3, and so on. That’s it. No tricks, no fancy integration, just straightforward addition for whatever configuration you’ve got lined up.

Equipotential surfaces? Think of them like contour lines on a map—every point along one of these surfaces sits at the exact same potential. No surprises there. And here’s the kicker: electric field lines never run along them. They cut straight through, always perpendicular, always at a right angle. That’s just how the physics shakes out.

Capacitance and Capacitors

Capacitors are basically just two conductors working together to stash away charge. That’s their whole deal. The capacitance, which we write as C, tells you how much charge they can actually hold—it’s the storing capacity. And the math is pretty clean: C equals Q over V. For a parallel plate capacitor, the formula shifts a little: C equals ε₀A over d. Here, A is the area of the plates, and d is the gap between them. Simple enough, right?

Combination of Capacitors

Capacitors ko combine karna ho toh aapke paas do basic options hain—series ya parallel. Aur sach kahun toh har ek ka apna alag logic hai, apni alag math hai. Series mein total capacitance kam ho jaati hai, jabki parallel mein woh badh jaati hai. Yeh dono tarike apni jagah kaam aate hain, bas zaroorat hoti hai samajhne ki kis situation mein kaunsa sahi rahega.

• Series combination works a bit differently. The equation looks like this: 1/C_eq = 1/C1 + 1/C2 + 1/C3 and so on. And here's the kicker—charge stays the same throughout. Yep, same charge, no matter which capacitor you're looking at.
• Parallel combination: C_eq = C1 + C2 + C3 +... Here, the potential difference stays the same across all of them.

Energy in Capacitors

Ek charged capacitor ke andar jo energy chhupi hoti hai, usse hum likhte hain U = (1/2)CV², ya phir U = (1/2)Q²/C, aur agar chahein toh U = (1/2)QV bhi keh sakte hain. Ye teeno expressions ek hi cheez bolte hain — bas alag-alag variables ke through. Asal mein, ye energy kahin aur nahi, electric field ke bheetar hi store rehti hai. Ab agar tum us capacitor ke beech mein koi dielectric material daal do, toh capacitance badh jaati hai. Iska formula simple hai: C = kC₀, jahan pe k dielectric constant ka naam hai. Toh seedhi baat — dielectric daalo, capacitance badhao, aur energy ka hisaab wahi rehta hai.

Important NCERT Problems Solved

When you sit down to solve those end-of-chapter numericals, don’t just dive in blind. Work through them step by step. First, jot down every piece of given data—yes, even the obvious stuff. Next, figure out which formula actually fits the problem. Then, plug your values in carefully, and don’t forget to write the final answer with its unit. Let’s make it concrete. Say you’ve got two charges, +5μC and -3μC, placed 16 cm apart. You need the electric potential right at their midpoint. So, the formula is V_total = k[q1/(r/2) + q2/(r/2)]. Crunch the numbers and you’ll land on 2.25 x 10^5 V. That’s it—simple once you keep the steps straight.

Practice these solutions thoroughly—seriously, it’ll pay off big time when board exams roll around. Don’t just read them; grab a pen, work through each step yourself. And for every concept, try to pair it with a diagram. Draw it out, label it, mess it up and redraw it. That visual connection makes things stick in a way plain text never will. Trust me, this habit alone can save you marks in the exam hall.