Lorentz force on an electron An electron of charge −e moves with velocity v in simultaneous electric field E and magnetic flux density B. Is the force given by F = −e (E + v × B)?

Introduction / Context:
The Lorentz force law is the foundation of electromagnetics and beam physics. For a particle with charge q, the total electromagnetic force is q (E + v × B). The sign of q matters, so for an electron (q = −e), the force reverses direction relative to a positive charge.

Given Data / Assumptions:

• Particle is an electron with charge −e.
• Fields are E (electric) and B (magnetic flux density).
• Classical, non-relativistic expression is adequate.

Concept / Approach:

Start with F = q (E + v × B). Substitute q = −e to get F = −e (E + v × B). This holds regardless of the relative orientation of v and B and in vacuum or material media (as a local equation of motion for the particle).

Step-by-Step Solution:

Verification / Alternative check:

Right-hand-rule cross products correctly predict curvature direction in magnetic fields for positive charges; electrons curve oppositely because q is negative, consistent with the formula.

Why Other Options Are Wrong:

• Restrictions like v ⟂ B or “in vacuum only” are unnecessary; the law is general.

Common Pitfalls:

Forgetting the negative sign for electrons; mixing H and B (the Lorentz force uses B).

Final Answer:

True