Magnetic field lines — can they intersect? State whether the following is true or false: “Lines of magnetic field cannot intersect one another at a point.”

Introduction / Context:
Field lines are a visualization tool to represent vector fields like the magnetic flux density B. Though not physical objects, they obey strict rules derived from the uniqueness of vector direction at each point in space.

Given Data / Assumptions:

• Static or quasi-static magnetic field representation.
• Continuous, single-valued B-vector field.
• No magnetic monopoles (∇ · B = 0).

Concept / Approach:
At any given point, a vector field has a single direction. If two field lines were to intersect, it would imply two different directions for B at the same point, which is impossible. Therefore, correctly drawn magnetic field lines never cross.

Step-by-Step Solution:
Define field line: a curve whose tangent at each point is parallel to B.Assume intersection at a point; then there are two tangents → two directions.Contradiction with single-valued B → intersection cannot occur → statement true.

Verification / Alternative check:
Mathematical uniqueness of solutions to magnetostatic boundary-value problems ensures a well-defined B-field direction at each point, consistent with non-intersecting lines.

Why Other Options Are Wrong:
“False” options contradict the geometric definition. The statement holds in free space and materials alike. Calling lines “imaginary” does not negate the rule governing their construction.

Common Pitfalls:

• Misreading crowded diagrams as intersections; properly they are closely spaced but non-crossing.
• Confusing field line density (magnitude) with direction properties.

Final Answer:
True