The line integral of the magnetic field intensity is given by the current element.

Explanation:

Line integral is a concept in mathematics that involves calculating the integral of a function along a curve or path. In the case of the magnetic field intensity, the line integral is used to calculate the magnetic field strength along a particular path.

The magnetic field intensity, also known as H-field, is a measure of the magnetizing force or magnetic field strength. It is represented by the symbol H and has units of ampere per meter (A/m). The H-field is related to the magnetic flux density, also known as B-field, through the permeability of the medium.

The magnetic flux density, represented by the symbol B, is a measure of the magnetic field's strength or the amount of magnetic flux per unit area. It has units of Tesla (T) or Weber per square meter (Wb/m²).

To calculate the line integral of the magnetic field intensity, we consider a current element. A current element is a small segment of a current-carrying conductor. It is defined as the product of the current flowing through the conductor and the length of the element.

The line integral of the magnetic field intensity along a closed path is given by Ampere's circuital law. According to this law, the line integral of H-field around a closed loop is equal to the total current passing through the loop. Mathematically, it can be expressed as:

∮H · dl = I,

where ∮ represents the line integral, H is the magnetic field intensity, dl is an infinitesimal length element along the path, and I is the total current passing through the loop.

Therefore, the line integral of the magnetic field intensity is given by the current element, which represents the total current passing through the loop. This relationship allows us to calculate the magnetic field intensity at any point on the loop by considering the current flowing through it.

In summary, the line integral of the magnetic field intensity is given by the current element, representing the total current passing through a closed loop. This relationship is described by Ampere's circuital law and is used to determine the magnetic field strength along a particular path.