Lista 3 - Física 3 Resolvida

Fisica 3 - Lista 3\n1) \\epsilon = 8.10^6 V/m\nd = 0.5 m\na) \\Delta V = \\int E dx\n\\Delta V = \\int 8.10^6 dz\n\\Delta V = 8.10^6 * 0.5\n\\Delta V = 4.10^6 V\nb) V = U/q\n\\Delta V = -9.10^1 U\nU = 6.94 * 10^(-15)\n\n2) q1 = 31 \\mu C\nm = 20 mg\nR1 = 0.9 mm\nR2 = 2.5 mm\n\\epsilon_initial = \\epsilon\nE_i + E_1 + E_{q1} + E_{q2}\n0 + E_i + E_q + E_{q1}\n\n\\left( \\frac{K q^2}{R_1} + \\frac{H q^2}{R_2} \\right) = Ec / \\left( \\frac{1}{R_1} \\right)\n\\left( \\frac{m v^2}{k q^2} \\right) \n2 = \\frac{2.5.10^3 m/s^2}{R_1 R_2}\n3) q2 = 20 nC\nq2 = 20 nC\n\n3) q3 = 20 nC\na) V = K q1 q2 / x\nV = \\frac{K q2}{x x}\nU = 3.8.10^(-10) q2\nb) U = 89 q3\n\n4) V = K q / R\n\\cos \\theta = \\frac{3}{\\sqrt{R^2}}\nV = K \\phi q \\cos \\theta\nV = K \\phi q \\left( \\frac{x^2}{x^2 + 3^2} \\right)^{3/2}\n5) q3 = 30 pC\na) V = K Q\nR = R_1 (8.99.10^9 10^(-12)) / R\n= 0.54 mm\n\n\\sqrt{V^2} = 2 \\pi R^n \\frac{R^2}{3}\n= 2 \\pi R R^2 \\cdot R^{-1/2}\n6) \\epsilon = 0.10 \\mu C/cm^2\nV = -K / \\Delta V\n\\Delta V = \\frac{-6}{2 \\epsilon}\n\\Delta z_3 = -\\Delta V / \\epsilon_0 = 8.88 mm 4) V = K q \\rho \\cos \\theta\n\\cos \\theta = \\frac{3}{R \\sqrt{3 x^2}}\n\\Rightarrow V = \\frac{K \\rho}{\\left( x^2 + 3^2 \\right)^{3/2}}\\n\nE_x = -\\frac{dV}{dx} = -k q \\cdot d\ndx = -k p \\cdot 2x\n\\Rightarrow E_3 = -k q_1 \\;\n\\Rightarrow E_x = k_p \\left(3x^3 - \\frac{4}{(x^2 + 3^2)^{3/2}}\\right)\n5) q3 = 30 nC\na) V = K Q\n\\quad R = 500\n\\Rightarrow\\sqrt{V^2} = \\frac{4 \\pi R}{3}\n6) V = k( q_0 \\frac{1}{R^2} ) \\approx \\sqrt{( 8.99.10^9 \\cdot 10^{-12})/R^{3/2} }\n= 793 V 7) Potencial da carga\n\\Delta V = \\frac{q}{4 \\pi \\epsilon}\n\\Delta V = \\frac{-V_{ext} - V_{lab} - k_e}{d}\n\\Rightarrow V = V + K / 2\ndad\\left(8 \\cdot \\frac{q_1}{\\rho^2} \\, k g \\right) dx \\;\;\n\\Rightarrow U_{in} = \\sum \\frac{k_e q}{R^2} \\, j_i k_j \n8) a) x > R \\\\ z_i = <e^2>\\n= \\frac{K}{k q} + \\frac{1}{4}\n\\frac{1}{d} \\; dx = \\frac{F_L}{R^2}\nV(r) = -\\int \\int E_r d\\theta\\;\n\\Rightarrow V(r) = \\frac{K g q 3 - k_i^2}{2R^2} 1) a) A = A_x\n dV / dA = k dθ ( 0 )\nV = k A [ L² + y² ]½ \ndV /\n\ny V = k A [ 1 - y² / y_i²]\n \nc) Não têm a, não há associação de q, portanto não passou cálculo.\n\n10) q = -g_in C\n R = 1.5 m\nV(z) = k Q\n [3 + 4 R²]\nW = -ΔU\n(U_i, V.q)\n3 = 3\n3 = 0\ndq = 6ρc\n\nV_i = k_q Q\n\t -1.2e^{-4}\nV_2 = k q Q\n\t -1.0 / R²\nU_1 = 1.495 × 10^{-13}\nU_2 = 324 × 10^{-13}\nW = -324 μJ - 145 μJ = -179 pJ 1) a) V = k [ 1.0 × 10^3 - ( -3.1 × 10^9 ) - 8.0 × 10^2 - ( -2 ) 10^5 - 180 V ]\n1 \n1) V_i = H_q = 2.0 × 10^{-4} × (1.0 × 10^{4}) = 3000 V\n \nV_f = 9 × 10^6 ( 3 × 10^{-9} ) / 3 × 10^{-2}\n \nV_f = -3000 V\n\n2) a) \u221A (kg) = 9.1 × 10^9 (5.0 × 10^9 )², 0.225 J\n d = 1.00\n\n4) F = H_q² / d² = 0.225 J\n a_a = F / m_a = ( 45.0 m / s² ) \n \n w_a = F_m = 82.5 m / s²\n\nc) U_i + U_f = k × h → U_i = mv² + mgh\n 2 2\n \nmin = m + mv_i² = -m_vel + m_gy + m*z / p\n0: m_i v_i + m_b v_B → -m_A v_A → v_B = 0.387 m / B\nG U_i = (m_a + m_b) / m_a → U_f = 7.75 m / m_b