Magnetic Material and Equation

A magnetic material is characterized by the presence of microscopic magnetic domains that are oriented in a particular direction. These domains are responsible for the magnetic properties of the material. The behavior of magnetic materials can be described using various mathematical equations, including the line integral of H, surface integral of H, line integral of B, and surface integral of B.

Surface Integral of B is Zero

The correct equation that holds good for a magnetic material is the surface integral of B is zero. This equation is also known as Gauss's law for magnetism, and it states that the total magnetic flux through any closed surface is zero. Mathematically, it can be expressed as:

∮S B.dS = 0

Where ∮S represents the surface integral, B is the magnetic field, and dS is the differential element of the surface.

Explanation

The surface integral of B is zero because magnetic monopoles do not exist. Unlike electric charges, which can be either positive or negative, magnetic charges (or magnetic monopoles) always come in pairs of north and south poles. This means that the net magnetic flux through any closed surface must be zero since the magnetic field lines always form complete loops.

Moreover, the surface integral of B is related to the total current passing through the surface, as described by Ampere's law. Therefore, if the surface integral of B is zero, it implies that there is no net current passing through the surface. This is consistent with the behavior of magnetic materials, which do not have any net magnetic charges or currents.

Conclusion

In summary, the equation that holds good for a magnetic material is the surface integral of B is zero. This equation is a consequence of the absence of magnetic monopoles and is consistent with the behavior of magnetic materials, which do not have any net magnetic charges or currents.