- #1
phantomvommand
- 271
- 39
- Homework Statement
- I am trying to use the Lorentz Force formula to derive v = E/B. What is wrong with my working?
- Relevant Equations
- ##F = q(\mathbf E + \mathbf v \times \mathbf B)##
Suppose the E-field is ##-E_y\hat y##, and B-field is ##B\hat z##. Mass is ##m##.
z
|
|_____x
/
y
##m(\ddot x \hat x + \ddot y \hat y) = q(-E_y \hat y + (v_x \hat x + v_y \hat y) \times B \hat z)##
By grouping terms with ##\hat x## and ##\hat y## together,
##m\ddot x = -qv_yB##
##m\ddot y = q(v_xB - E_y)##
Set ##\ddot x = 0, \ddot y = 0##,
##-v_yB = v_xB - E_y##.
Why don't I get ## v = \frac E B##?
z
|
|_____x
/
y
##m(\ddot x \hat x + \ddot y \hat y) = q(-E_y \hat y + (v_x \hat x + v_y \hat y) \times B \hat z)##
By grouping terms with ##\hat x## and ##\hat y## together,
##m\ddot x = -qv_yB##
##m\ddot y = q(v_xB - E_y)##
Set ##\ddot x = 0, \ddot y = 0##,
##-v_yB = v_xB - E_y##.
Why don't I get ## v = \frac E B##?
Last edited: