How Does an Electron Move in a Magnetic Field Within a Cloud Chamber?

[DiamondGeezer]

An electron enters a cloud chamber which has a magnetic field B but the path of the electron is not perpendicular to the magnetic field. I understand that the electron path will describe a spiral.

Does the v in the equation F = q(v x B) refer to the component of the electron's velocity which is perpendicular to the B field? Can I assume that an electron's velocity parallel to the B field remains constant and is unaffected by the B field?

 

[jtbell]

The $\vec v$ in that equation is the vector velocity of the electron, including all three (x, y, z) components in general. However, you're correct that the component of $\vec v$ parallel to $\vec B$ does not contribute to $\vec F$. So if, for example, $\vec B$ is in the z-direction (i.e. $B_x = B_y = 0$), then it doesn't matter what $v_z$ is, as far as $\vec F$ is concerned:

$$F_x = q (v_y B_z - v_z B_y)$$

$$F_y = q (v_z B_x - v_x B_z)$$

$$F_z = q (v_x B_y - v_y B_x)$$

 

[DiamondGeezer]

Thank you. That completely answers my question

 

[Meir Achuz]

But it is a helix, not a spiral.

 

[DiamondGeezer]

But it is a helix, not a spiral.

Correct.