Which statement about motional emf is true?

Which statement about motional emf is true?

• A. It is independent of the magnetic field.
• B. It is proportional to B, L, and v.
• C. It is inversely proportional to L.
• D. It depends only on the area of the circuit.

Answer: (B)

When a conductor moves through a magnetic field, charges inside feel a magnetic force q(v × B) that pushes them along the length of the conductor. This separation of charges creates an electric potential difference, an emf, across the ends of the moving piece. For a straight rod of length L moving with speed v in a uniform B field, and with the motion and field arranged so the rod feels a force along its length, the emf magnitude is ε = B L v (more generally ε = B L v sin φ if the velocity is not exactly perpendicular to B). This shows why the emf grows with the magnetic field strength, the length of the conductor, and its speed. It’s not independent of the field, and it’s not inversely proportional to the length. It also isn’t determined solely by the area of the circuit—area matters in magnetic flux for stationary loops, but motional emf in this setup depends on B, L, and v.

When a conductor moves through a magnetic field, charges inside feel a magnetic force q(v × B) that pushes them along the length of the conductor. This separation of charges creates an electric potential difference, an emf, across the ends of the moving piece. For a straight rod of length L moving with speed v in a uniform B field, and with the motion and field arranged so the rod feels a force along its length, the emf magnitude is ε = B L v (more generally ε = B L v sin φ if the velocity is not exactly perpendicular to B).

This shows why the emf grows with the magnetic field strength, the length of the conductor, and its speed. It’s not independent of the field, and it’s not inversely proportional to the length. It also isn’t determined solely by the area of the circuit—area matters in magnetic flux for stationary loops, but motional emf in this setup depends on B, L, and v.