Physics 321 Hour 4 Lorentz Force
Lorentz Force 𝐹 =𝑞 𝑣 × 𝐵 𝑚 𝑥 𝑚 𝑦 𝑚 𝑧 = 𝑞 𝑦 𝐵 𝑧 − 𝑧 𝐵 𝑦 𝑞 𝑧 𝐵 𝑥 − 𝑥 𝐵 𝑧 𝑞 𝑥 𝐵 𝑦 − 𝑦 𝐵 𝑥 or 𝑚 𝑣 𝑥 𝑚 𝑣 𝑦 𝑚 𝑣 𝑧 = 𝑞 𝑣 𝑦 𝐵 𝑧 − 𝑣 𝑧 𝐵 𝑦 𝑞 𝑣 𝑧 𝐵 𝑥 − 𝑣 𝑥 𝐵 𝑧 𝑞 𝑣 𝑥 𝐵 𝑦 − 𝑣 𝑦 𝐵 𝑥 , 𝑣 𝑥 𝑣 𝑦 𝑣 𝑧 = 𝑥 𝑦 𝑧 Gottfried Wilhem von Leibiz
𝑚 𝑣 𝑥 𝑚 𝑣 𝑦 𝑚 𝑣 𝑧 = 𝑞 𝑣 𝑦 𝐵 −𝑞 𝑣 𝑥 𝐵 0 , 𝑣 𝑥 𝑣 𝑦 𝑣 𝑧 = 𝑥 𝑦 𝑧 Lorentz Force If 𝐵 is a constant, without loss of generality we can choose 𝐵 =𝐵 𝑧 . 𝐹 =𝑞 𝑣 × 𝐵 𝑚 𝑥 𝑚 𝑦 𝑚 𝑧 = 𝑞 𝑦 𝐵 −𝑞 𝑥 𝐵 0 or 𝑚 𝑣 𝑥 𝑚 𝑣 𝑦 𝑚 𝑣 𝑧 = 𝑞 𝑣 𝑦 𝐵 −𝑞 𝑣 𝑥 𝐵 0 , 𝑣 𝑥 𝑣 𝑦 𝑣 𝑧 = 𝑥 𝑦 𝑧 Gottfried Wilhem von Leibiz
Mathematica Lorentz.nb Gottfried Wilhem von Leibiz