Explanation:

Tangential Flux Density:
- Tangential flux density refers to the component of flux density parallel to the surface boundary.
- In the context of electromagnetics, it is important to consider the continuity of tangential flux density at boundaries.

Continuity of Tangential Flux Density:
- The statement that the tangential component of flux density is continuous at the boundary is true.
- This is based on the principle of electromagnetic field behavior at interfaces.
- When there is a boundary between two different materials or mediums, the tangential component of the flux density remains continuous across the boundary.

Explanation:
- The continuity of tangential flux density at boundaries is a consequence of Maxwell's equations and the conservation of electromagnetic field lines.
- This continuity ensures that there are no abrupt changes or discontinuities in the tangential component of flux density at the interface.
- It is fundamental to the understanding and analysis of electromagnetic fields and their behavior at material boundaries.

Importance:
- The continuity of tangential flux density plays a crucial role in the design and analysis of various electromagnetic devices and systems.
- It helps in predicting the behavior of electromagnetic fields at boundaries and interfaces, which is essential for optimizing the performance of such systems.
Therefore, the statement that the tangential component of flux density is continuous at the boundary is true, and it is a fundamental concept in the study of electromagnetics.