Question

Suppose you take a short piece of wire that is not attached to anything and move it up and down in a magnetic field. Explain whether or not a current will be induced, and why.

Answer 1

No. Moving a single isolated straight piece of wire up and down in a steady magnetic field does not produce a continuous conduction current, because there is no closed circuit for a current to flow through.

Why:
- Faraday's law gives an emf around a closed loop: ∮E·dl = −dΦ/dt. If there is no loop, there is no closed-path emf to drive a steady current.
- Moving charges in the wire feel the magnetic Lorentz force q(v×B). That pushes charges to the ends of the wire, producing a transient redistribution (polarization) and a potential difference between the ends (for a rod of length L, ε ≈ B L v for the usual perpendicular geometry). This charge motion is brief; it stops when the internal electric field balances q(v×B), so no steady current flows.
- If you connect the ends to form a closed circuit (or attach the rod to rails), that motional emf will drive a current I = ε/R. In the isolated case only a short transient and a static end-to-end voltage result, not a sustained current.