Faraday–Lenz intuition: When the speed of a conductor moving through a magnetic field is increased, how does the induced voltage respond?

Introduction / Context:Motional electromotive force (emf) underpins generators and many sensors. The induced voltage depends on geometry, field strength, and the relative speed between a conductor and the magnetic field. Recognizing these proportionalities helps predict system behavior when mechanical speed changes.

Given Data / Assumptions:

• Uniform magnetic field B.
• A straight conductor of effective length l moving with speed v perpendicular to B for maximum effect.
• Linear, non-saturating regime without end effects.

Concept / Approach:The motional emf formula is emf = B * l * v * sin(θ), with θ the angle between velocity and the field. For the perpendicular case (θ = 90°, sin θ = 1), emf ∝ v. Increasing speed v therefore increases the induced voltage proportionally.

Step-by-Step Solution:

Verification / Alternative check:Generator behavior: Raising rotor speed increases generated voltage at constant field excitation. Similarly, moving a wire faster through a field yields higher galvanometer deflection (higher induced emf) in classroom demonstrations.

Why Other Options Are Wrong:

• Remains constant: Only true if speed and effective flux cutting remain constant.
• Decreases or Reaches zero: Opposite of the speed dependence; zero would require v = 0 or no effective flux cutting.

Common Pitfalls:

• Forgetting the sin(θ) factor; with non-perpendicular motion, the increase still scales with the perpendicular component of v.
• Confusing transformer emf (from dΦ/dt) with motional emf (from v across B).

Final Answer:increases