Coulomb’s Law Advanced Problems | Equilibrium & SHM | Electrostatics L4 | CBSE 12 & JEE Main скачать в хорошем качестве

Coulomb’s Law Advanced Problems | Equilibrium & SHM | Electrostatics L4 | CBSE 12 & JEE Main

In this video (Electrostatics – Lecture 4: Coulomb’s Law, Advanced Equilibrium & Applications), we solve four high‑quality problems that use Coulomb’s law together with force balance and geometry. These are exactly the type of questions that deepen your understanding and are highly relevant for CBSE Class 12 boards and JEE Main level. What we cover in this lecture: • Q1: Three identical charges in equilibrium – Three equal masses, each with charge q, suspended by strings of length L – Charges form an equilateral triangle of side a in equilibrium – Vertical and horizontal force balance – Using geometry (projection of triangle, OA, OP) and L ≫ a approximation – Result: expression for charge q in terms of m, g, a, L and ε₀ • Q2: Two unequal masses with charges at the same horizontal level – Masses 2m and m, both positively charged, suspended from a common point – Strings at different angles, but lower ends at same vertical level – Free body diagrams and tanθ relations for each mass – Using tan(θ₁ + θ₂) with θ₁ + θ₂ = 45° – Solving quadratic to find electrostatic force F between them • Q3: Charge above the centre of a charged square in equilibrium – Four equal charges Q at corners of a square of side l – Unit positive charge (mass m) placed at height h above the centre – Symmetry argument: horizontal components cancel, vertical add – Using geometry to relate cosθ and the distance from corners – Condition for equilibrium: net electric force = mg – Final expression for Q in terms of m, g, h, l and k (or ε₀) • Q4: SHM of a charged particle on the axis of a charged ring – Ring of radius a with total positive charge q – Particle of mass m, charge −Q placed on axis at distance x (x ≪ a) – Integrating the force due to ring charge elements – Exact axial force expression and small‑x expansion – Approximating F ≈ −kx and identifying k – Time period of small oscillations: ( T = 2\pi\sqrt{\dfrac{4\pi\varepsilon_0 m a^3}{qQ}} ) Key ideas reinforced: • Coulomb’s law in vector form and symmetry • Force balance and resolving into components • Use of geometry and trigonometry in Electrostatics • Small‑angle / small‑displacement approximations (L ≫ a, x ≪ a) • Connecting restoring force F = −kx to SHM and time period This lecture is ideal for: • CBSE Class 12 students revising Electrostatics numericals • JEE Main aspirants needing strong conceptual grip on Coulomb’s law applications • Anyone who wants step‑by‑step, rigorous yet calm explanations (slides + voice) If you find this helpful, continue with the full Electrostatics playlist where we go from Coulomb’s law to electric field, superposition, and potential in a systematic way. Channel: CBSE & JEE Physics | Dr Kedar Pathak