Field-line visualization: do magnetic field lines attract each other? Evaluate the statement: “Lines of magnetic field attract each other.” Choose the most accurate scientific assessment.

Introduction / Context:
Field lines are a convenient way to visualize vector fields such as magnetic flux density B. Misinterpreting these lines as physical objects can lead to incorrect reasoning about forces in electromagnetism.

Given Data / Assumptions:

• We are discussing classical magnetostatics.
• “Field lines” denote a plotting aid: tangents give the field direction; density indicates magnitude.
• No magnetic monopoles; ∇ · B = 0.

Concept / Approach:
Magnetic field lines are not physical strings that exert forces on each other. Forces act on currents, magnetic dipoles, and magnetizable media via the Lorentz force and magnetization energy gradients, not between abstract lines. Patterns that appear as “bunching” arise because materials (e.g., ferromagnets) increase B inside them due to high permeability, not because lines attract.

Step-by-Step Solution:
Clarify definition: field lines visualize B; they lack independent dynamics.Explain observed “crowding”: in high-μ materials, B = μH becomes large, so plotted lines are denser inside.Conclude: the statement about attraction between lines is false; interactions occur through fields and matter, not line–line forces.

Verification / Alternative check:
Mathematically, superposition of fields is linear in vacuum. There is no term implying self-interaction of B lines in Maxwell’s equations.

Why Other Options Are Wrong:
Claiming the statement becomes true in vacuum, ferromagnets, or strong fields assigns physical agency to a plotting tool. The visual crowding is a consequence of material response, not attraction of lines.

Common Pitfalls:
Interpreting iron-filing patterns as lines that pull each other; filings simply align with local B and trace its distribution.

Final Answer:
False (field lines are a graphical construct; they neither attract nor repel)