A stationary charge, Q, is placed in the middle of a magnetic field, B, and electric field, E. The magnetic field and the electric field are perpendicular to each other. What is the ratio of the force on Q caused by the magnetic field and the force caused by the electric field, [math: FBFE]?

Question

BlackTom AI · Accepted Answer

Magnetic force on a point charge depends on its velocity, while the electric force depends directly on the charge and the electric field: these are the central concepts.

1) Relevant knowledge points and concepts
- Magnetic (Lorentz) force on a charge: F_B = q (v × B), magnitude F_B = q v B sinθ. It requires the charge to be moving (v ≠ 0).
- Electric force on a charge: F_E = q E, independent of the charge’s velocity.
- For a stationary charge, v = 0, so the magnetic force is zero regardless of B or the angle between fields.

2) Step-by-step reasoning
- The charge Q is stationary, so its velocity v = 0.
- Substitute v = 0 into the magnetic force formula: F_B = Q v B sinθ → F_B = Q · 0 · B · sinθ = 0.
- Compute the electric force: F_E = Q E (nonzero in general, unless E = 0, which is not stated).

3) Calculations (intermediate steps)
- F_B = Q v B sinθ = Q × 0 × B × sinθ = 0.
- F_E = Q E.
- Ratio F_B / F_E = 0 / (Q E) = 0.

4) Why the correct answer is correct
- Because the magnetic force on a charge is proportional to its velocity, a stationary charge experiences no magnetic force; the electric force is Q E, so the ratio of magnetic to electric force is zero.

5) Why the other options are incorrect
- B/(Q E), B/E, and BQ/E imply a nonzero magnetic force depending on B and/or Q; these neglect that v = 0. None account for the essential factor v = 0 that makes F_B vanish.

6) Conclusion
- Therefore the ratio F_B / F_E = 0, which matches the provided correct answer: 0.

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