The thrust exerted on a conductor in a magnetic field is give by the formula:

Question

BlackTom AI · Accepted Answer

Magnetic force on a current-carrying conductor is given by the Lorentz force applied to the moving charge carriers, so the magnitude can be written as F = B I l (for the conductor perpendicular to the magnetic field).

1. Relevant knowledge points and concepts
- Lorentz force on a single charge: Fsingle = q v × B. For perpendicular v and B, magnitude Fsingle = q v B.
- Current in a conductor arises from many charge carriers: I = n A q v (where n = charge carrier density, A = cross-sectional area, q = carrier charge, v = drift velocity).
- Force on the whole segment of length l is the sum of forces on all carriers, giving the net thrust on the conductor: F = B I l (more generally F = B I l sinθ if the conductor is at angle θ to B).
- Units check: Tesla·meter·Ampere = (N·s)/(C·m) · m · A → N, consistent.

2. Step-by-step reasoning and derivation
- Start with the force on one carrier: Fsingle = q v B (assuming perpendicular).
- Number of carriers in length l: N = n A l. Total force on all carriers: Ftotal = N · Fsingle = (n A l) · (q v B) = n A q v B l.
- Express current: I = n A q v. Substitute into Ftotal:
  F = (n A q v) B l = I B l.
- Therefore F = B I l (or F = B I l sinθ for general angle).

3. Intermediate steps shown above (substitution I = n A q v → F = I B l).

4. Why this is correct
- The derivation follows directly from Lorentz force and the definition of electric current. It yields a force proportional to magnetic flux density B, current I, and conductor length l in the field.

5. Why other options are incorrect
- "F = v B I L": introduces drift velocity v redundantly; since I already includes v (I = n A q v), this form double-counts and is not the standard expression for thrust on the conductor.
- "F = m a": Newton’s second law relates force to mass and acceleration but does not express the magnetic force on a current-carrying conductor in terms of B, I, and l.
- The fourth option "F = B l I" is the same as the correct expression (duplicate).

6. Conclusion
The correct expression for the thrust on a conductor in a magnetic field is F = B l I, matching the provided answer.

The thrust exerted on a conductor in a magnetic field is give by the formula:单项选择题

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