Electric Field of Symmetric Charge Systems + Charged Pendulum in Electric Field (JEE/CBSE) скачать в хорошем качестве

Electric Field of Symmetric Charge Systems + Charged Pendulum in Electric Field (JEE/CBSE)

Electric Charges and Fields – Lecture 7 Series: CBSE & JEE Physics | Class 12 + JEE Main Level Teacher: Dr. Kedar Pathak In this lecture we apply the superposition principle and symmetry to non‑trivial electric field problems: What we cover in this lecture: Electric field of a symmetric system (square of charges) Charges +q and –q placed at the vertices of a square Geometry of the square: side, diagonal, distance from centre to vertices Field at a point on the diagonal: using symmetry and vector resolution Components of electric field along diagonals AC and BD Net electric field magnitude: [ E_0 = \frac{2\sqrt{2},kq,l}{(x^2 + l^2)^{3/2}} ] Behaviour of the field: At the centre of the square Far away on the diagonal (dipole‑like behaviour) Concept check on symmetry (Q2) Limiting cases: (x \to 0) and (x \to \infty) Does the configuration behave like a point charge or a dipole at large distances? Charged pendulum in a uniform electric field Bob with mass (m), charge (q), length (l) in a uniform (\vec{E}) Free‑body diagram: weight (m\vec{g}) and electric force (q\vec{E}) Defining effective gravity: [ \vec{g}_{\text{eff}} = \frac{\vec{W} + \vec{F}_e}{m} ] Time period of small oscillations: [ T = 2\pi \sqrt{\frac{l}{g_{\text{eff}}}} ] Four important cases for the charged pendulum (Q3) (i) ( \vec{E} ) vertically down, ( E = \dfrac{mg}{q} ) (ii) ( \vec{E} ) vertically up, ( E = \dfrac{2mg}{q} ) (iii) ( \vec{E} ) horizontal, ( E = \dfrac{mg}{q} ) (iv) ( \vec{E} ) at (45^\circ) above horizontal, ( E = \dfrac{\sqrt{2}mg}{q} ) For each case: Orientation of pendulum at equilibrium Effective value of ( g_{\text{eff}} ) Time period ( T = 2\pi \sqrt{l/g_{\text{eff}}} ) Summary table Quick comparison of (g_{\text{eff}}) and time period in all four cases Concept check (Q4) Deriving (\tan\theta) for horizontal electric field Showing (\theta = 45^\circ) when (E = mg/q) Why time period depends only on (g_{\text{eff}}), not on the string’s orientation Level and Exam Mapping NCERT/CBSE Class 12: Superposition, field of multiple charges Application of electric field to equilibrium and oscillations JEE Main: Symmetry‑based field calculation for square of charges Charged pendulum in uniform electric field, effective gravity method Bonus / JEE Advanced flavour: Far‑field behaviour of charge configurations Thinking in terms of equivalent dipole Playlist / Series Info This is Lecture 7 in the Electrictrostatics playlist on the channel “CBSE & JEE Physics | Dr Kedar Pathak”. The series focuses on: Clean, step‑by‑step conceptual explanations Rigorous but exam‑oriented derivations If you find this helpful, explore the full playlist and consider subscribing for more lectures on CBSE 11–12 and JEE Main physics.