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Notes is very usefull for you Access our Purchase PDF download for Class 12 Physics Chapter 2: Electrostatic Potential And Capacitance. This chapter is about the fundamental concepts of electric charges, Coulomb's law, electric fields, and Gauss's law. Our detailed Notes provide clear explanations, essential formulas, and practical examples to help you grasp these concepts effectively and prepare thoroughly for your exams. Download the PDF now to get a valuable resource for your studies.
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Definition: Property of matter that causes it to experience a force when placed in an electric field. Types: Positive (+), Negative (−). Basic properties:
F=14πϵ0⋅∣q1q2∣r2F = \frac{1}{4\pi\epsilon_0} \cdot \frac{|q_1 q_2|}{r^2}F=4πϵ0 1 ⋅r2∣q1q2∣
Vector form:
F 12=14πϵ 0 ⋅q1q2r2r^12\vec{F}{12} = \frac{1}{4\pi\epsilon_0} \cdot \frac{q_1 q_2}{r^2} \hat{r}{12}F12=4πϵ0 1 ⋅r2q1q2r^
Key points: o Force is along the line joining charges. o Like charges repel, unlike charges attract. o ϵ0\epsilon_0ϵ0 (permittivity of free space) = 8.85×10−12 C2/N⋅m28.85 \times 10^{-12} , C^2/N·m^28.85×10−12C2/N⋅m2.
Net force on a charge = vector sum of individual forces due to all other charges.
Definition: Force per unit positive test charge.
E =F q0\vec{E} = \frac{\vec{F}}{q_0}E=q0F
Due to a point charge:
E=14πϵ0⋅qr2E = \frac{1}{4\pi\epsilon_0} \cdot \frac{q}{r^2}E=4πϵ0 1 ⋅r2q
Electric field lines: o Originate from + charges, terminate on − charges. o Never intersect. o Density of lines ∝ field strength.
Definition: Two equal and opposite charges separated by a small distance. Dipole moment:
p =q⋅d \vec{p} = q \cdot \vec{d}p=q⋅d
Field due to dipole: o Axial line: E=14πϵ0⋅2pr3E = \frac{1}{4\pi\epsilon_0} \cdot \frac{2p}{r^3}E=4πϵ0 1 ⋅r32p o Equatorial line: E=14πϵ0⋅pr3E = \frac{1}{4\pi\epsilon_0} \cdot \frac{p}{r^3}E=4πϵ0 1 ⋅r3p Torque in uniform field:
τ=pEsinθ \tau = pE \sin\thetaτ=pEsinθ
Linear charge density: λ=ql\lambda = \frac{q}{l}λ=lq Surface charge density: σ=qA\sigma = \frac{q}{A}σ=Aq Volume charge density: ρ=qV\rho = \frac{q}{V}ρ=Vq
∮E ⋅dA =qenclosedϵ0\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\epsilon_0}∮E⋅dA=ϵ0qenclosed
Useful for finding E \vec{E}E in symmetric charge distributions. Applications: o Field due to infinite line of charge. o Field inside/outside a uniformly charged sphere. o Field due to a uniformly charged infinite plane sheet.