Electric Charges and Fields 2024 Lecture Notes PDF

# YAKEEN 2.0 NEET 2024 - Lecture 09 by Abhishek Verma ## Today's Targets * Theory * Electric Field * Dipole * Gold-leaf Electroscope * Practice Questions * Dipole ## Sphere * **Solid Sphere** * Conducting: Charge on Surface * Non-Conducting: Charge on Volume * **Hollow Sphere** * Con...

# YAKEEN 2.0 NEET 2024 - Lecture 09 by Abhishek Verma ## Today's Targets * Theory * Electric Field * Dipole * Gold-leaf Electroscope * Practice Questions * Dipole ## Sphere * **Solid Sphere** * Conducting: Charge on Surface * Non-Conducting: Charge on Volume * **Hollow Sphere** * Conducting: Charge on its surface * Non-Conducting: Charge on its surface ## Electric Field Due To * **Solid Conducting Sphere:** σ = q/Area, q_in = 0 × 4πR² * **Hollow Conducting Sphere:** E = 0 * **Hollow Non-Conducting Sphere:** * Φ_E = q_in = σ × 4πR² * E = (q_in)/ε₀ = σ × 4πR²/ε₀ ## Electric Field Due To... * **Solid Conducting Sphere** * Φ = ∫E.dA = E ∫dA. * σ × 4πR²/ε₀ = E × 4πR² * E = σR²/ε₀R² * E = (σR²)/ε₀R² × 1/R * E = KQ/R² * **Non-Conducting solid sphere** * Φ = E∫dA. * Q/ε₀ = E × 4πr² * E = (KQ)/r² ## Electric Dipole * **Definition:** The sum of a small charge of equal magnitude but opposite nature, kept at a very small separation * **Magnitude:** |P| = magnitude × (Separation between them). * |P| = Qd * |P| = q(2l) * **Direction:** From negative charge to positive. * **Vector Quantity:** * **Unit:** C.m (debye) * **Practical Value:** 3.3 × 10^-30 cm ## Electric Field Due To Dipole Along Axis at Distance y * |E₁| = Kq/(y-l)² * |E₂| = Kq/(y+l)² * |E_net| = |E₁| - |E_net| * |E_net| = Kq/(y-l)² - Kq/(y+l)² * |E_net| = Kq/(y² - l²)² [ 2(2l × y) ] * |E_net| = (2KPy)/(y² - l²)² * E_axis = (2Kp)/(r³) when y >> l ## Electric Field Due To Dipole at Distance y from Equatorial Position * |E₁| = Kq/(y²+l²)^1/2 * |E₂| = Kq/(y²+l²)^1/2 * |E_net| = E.cos θ + E.cos θ * |E_net| = 2×( Kq/ (y²+l²)^1/2 × l / (y²+l²)^1/2) * |E_net| = (2Kq/ (y²+l²)^1/2 × l / (y²+l²)^1/2) * |E_net| = K(2q)l / (y²+l²)^3/2 ## Torque Due To Electrical Field on a Dipole * |P| = q (2l) * τ = 2Flsinθ * τ = 2qEl sinθ * τ = (2qEl)l * |τ| = |P|E sinθ ## Equilibrium of Dipole * τ = P × E * τ = E × P * |τ| = PEsinθ * 0°: τ_min (zero) * 180°: τ_min * 90°: τ_max = |P|E * U = - PE * 0°: U = -PE, Stable * 180°: U = PE, Unstable * U = PEsin θ ## Time Period of SHM Of Electric Dipole * τ = Iα * I = 2ml² * τ = -PEsinθ * 2ml² α = -PEsinθ * α = - (PE/ 2ml²) θ * ω² = PE/ 2ml² * ω = √(PE/ 2ml²) * T = 2π/ω * T = 2π√(2ml² / PE) ## MCQ Questions - Chapter: Electric Charge and Field 1. Three charges +4q, Q and q are placed in a straight line of length l at points 0, l/2 and l distance away from one end respectively. What should be Q in order to make the net force on q to be zero? * -q * 4q * -q/2 * -2q 2. A particle of mass m and carrying charge -q₁ is moving around a charge +q2 along a circular path of radius r. Find period of revolution of the charge –q1. * 16π³ε₀mr³/q₁q₂ * 8π³ε₀mr³/q₁q₂ * q₁q₂ / 16π³ε₀mr³ * Zero 3. Consider three point objects P, Q and R. P and Q repel each other, while P and R attract. What is the nature of force between Q and R? * Repulsive force * **Attractive force** * No force * None of these 4. The electric field intensity at a point in vacuum is equal to * Zero * Force a proton would experience there * Force an electron would experience there * **Force a unit positive charge would experience there** 5. A sphere of radius r has electric charge uniformly distributed in its entire volume. At a distance d from the centre inside the sphere (d < r) the electric field intensity is directly proportional to * 1/d * 1/d² * **d** * d² 6. The electric field at 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance R/2 from the centre will be * Zero * **2E** * 4E * 16E 7. In a uniform electric field if a charge is fired in a direction different from the line of electric field then the trajectory of the charge will be a * Straight line * Circle * **Parabola** * Ellipse The document shows the notes for a physics lecture about electric field due to different shapes like spheres and dipole. It includes explanations about forces, torque, equilibrium, time period and includes multichoice questions about these topics.