Transcript Physics 321 Hour 4 Lorentz Force

Physics 321
Hour 4
Lorentz Force
Lorentz Force
𝑚𝑣𝑥
𝑚𝑣𝑦
𝑚𝑣𝑧
=
𝐹 = 𝑞𝑣 × 𝐵
𝑞 𝑦𝐵𝑧 − 𝑧𝐵𝑦
𝑚𝑥
𝑚𝑦 = 𝑞 𝑧𝐵𝑥 − 𝑥𝐵𝑧
𝑚𝑧
𝑞 𝑥𝐵𝑦 − 𝑦𝐵𝑥
or
𝑞 𝑣𝑦 𝐵𝑧 − 𝑣𝑧 𝐵𝑦
𝑞 𝑣𝑧 𝐵𝑥 − 𝑣𝑥 𝐵𝑧 ,
𝑞 𝑣𝑥 𝐵𝑦 − 𝑣𝑦 𝐵𝑥
𝑣𝑥
𝑥
𝑣𝑦 = 𝑦
𝑣𝑧
𝑧
Lorentz Force
If 𝐵 is a constant, without loss of generality we can
choose 𝐵 = 𝐵𝑧.
𝐹 = 𝑞𝑣 × 𝐵
𝑞 𝑦𝐵
𝑚𝑥
𝑚𝑦 = −𝑞 𝑥𝐵
𝑚𝑧
0
or
𝑚𝑣𝑥
𝑣𝑥
𝑞𝑣𝑦 𝐵
𝑥
𝑣𝑦 = 𝑦
𝑚𝑣𝑦 = −𝑞𝑣𝑥 𝐵 ,
𝑣𝑧
𝑚𝑣𝑧
𝑧
0
Mathematica
Lorentz.nb