Questions: Magnetic Force on Current-Carrying Wires

Question 1

Two parallel wires are separated by 5 cm. Wire A carries current flowing north; wire B carries current flowing south. What is the magnetic interaction between them?

• A. They attract each other — current flow in any direction creates mutual attraction between wires
• B. They repel each other — antiparallel currents produce a repulsive force
• C. No force acts between them because the magnetic fields from each wire cancel at the other's location
• D. They attract if currents are equal in magnitude, repel if the magnitudes differ

Answer: (B)

Antiparallel currents (flowing in opposite directions) produce repulsion. Wire A creates a magnetic field that circles around it; at wire B's location this field points in a direction such that F = IL × B pushes wire B away from wire A. You can verify with the right-hand rule: curl your fingers around wire A in the direction of its field, then apply the force rule to wire B. Parallel currents attract; antiparallel currents repel. Options A and D ignore the directional dependence of the cross product.

Question 2

A straight wire carrying current I is oriented parallel to a uniform magnetic field B. What is the magnetic force on the wire?

• A. F = ILB, directed perpendicular to both the wire and the field
• B. F = ILB, directed along the wire in the direction of current flow
• C. F = 0, because the wire is parallel to the field
• D. F = ILB/2, reduced by half because the geometry is non-perpendicular

Answer: (C)

The force on a wire is F = ILB sinθ where θ is the angle between the wire direction and field B. When the wire is parallel to B, θ = 0° and sin(0°) = 0, so F = 0. Physically, the drifting electrons in the wire are moving parallel to B, so v × B = 0 (a vector crossed with a parallel vector is zero). The Lorentz force only acts when velocity has a component perpendicular to the field. Options A and D incorrectly assume a nonzero force, and option B gives the wrong direction even if force were nonzero.

Question 3

The force between two parallel current-carrying wires arises because wire 1's magnetic field exerts a Lorentz force on the moving charges (current) in wire 2.

• T. True
• F. False

Answer: True

This is the conceptual bridge between dF = I(dL × B) and the Lorentz force F = qv × B. Wire 1 creates a magnetic field at wire 2's location (by Ampere's law, curling around wire 1). The conduction electrons drifting through wire 2 are moving charges in that field, so each experiences a Lorentz force. Summing over all the charges in a wire segment gives dF = I(dL × B). The force between wires is not a new phenomenon — it is the Lorentz force applied to bulk current.

Question 4

Doubling the separation between two parallel current-carrying wires doubles the force per unit length between them.

• T. True
• F. False

Answer: False

The force per unit length is F/L = μ₀I₁I₂/(2πd). Doubling d (from d to 2d) gives F/L = μ₀I₁I₂/(2π·2d) = half the original force. The relationship is inverse, not direct: greater separation means weaker force. This follows from the fact that the magnetic field of an infinite straight wire falls off as 1/r. Doubling the distance halves the field strength at wire 2's location, which halves the force on wire 2.

Question 5

Explain why a wire carrying current perpendicular to a magnetic field experiences maximum force, while a wire parallel to the field experiences no force.

Model answer: The force on a wire segment is F = ILB sinθ, where θ is the angle between the current direction and B. When perpendicular (θ = 90°), sinθ = 1 and force is maximum F = ILB. When parallel (θ = 0°), sinθ = 0 and force is zero. The physical reason is the cross product in dF = I(dL × B): a vector crossed with a parallel vector is zero because there is no perpendicular component to generate a force. The drifting electrons in the wire only experience a Lorentz force when their velocity has a component perpendicular to B.

This directly follows from the vector nature of the Lorentz force. The cross product v × B measures the component of v perpendicular to B — that is the only component that contributes to the magnetic force. When v is parallel to B, there is no perpendicular component and the force vanishes entirely. When v is perpendicular to B, the full magnitude is available. For a wire, v is fixed in the direction of current flow, so the geometry of how the wire is oriented relative to B completely determines the force magnitude.