Questions: Complete Lorentz Force Law and Maxwell's Framework
2 questions to test your understanding
Score: 0 / 2
Question 1 Short Answer
A proton moves in the +x direction with speed v in a magnetic field pointing in the +z direction. What is the direction of the magnetic force on the proton?
Think about your answer, then reveal below.
Model answer: The force is in the −y direction. F⃗ = qv⃗ × B⃗ = q(v x̂) × (B ẑ) = qvB (x̂ × ẑ) = qvB(−ŷ). Since q > 0 for a proton, the force points in −y.
Use the right-hand rule for the cross product x̂ × ẑ = −ŷ (or equivalently, ẑ × x̂ = ŷ, so x̂ × ẑ = −ŷ). The result is perpendicular to both the velocity and the field, confirming that the magnetic force does no work — it curves the proton into circular motion in the x-y plane.
Question 2 Short Answer
Which of Maxwell's equations was modified by Maxwell himself (relative to its pre-Maxwell form), and what physical consequence did this modification enable?
Think about your answer, then reveal below.
Model answer: Ampere's law was modified by adding the displacement current term μ₀ε₀ ∂E⃗/∂t. This made the equations self-consistent with charge conservation and, crucially, allowed the derivation of electromagnetic waves propagating through vacuum at the speed of light.
Without the displacement current, a contradiction arose in circuits with capacitors: the original Ampere's law predicted a magnetic field around a wire carrying current, but gave inconsistent results when the surface bounding the Amperian loop was chosen to pass through a capacitor gap (where no current flows). The displacement current term resolved this inconsistency and had the momentous side effect of predicting that light is an electromagnetic wave.