True

The magnetic flux density (B) is directly proportional to the magnetic field intensity (H). This relationship is governed by Ampere's law, one of the fundamental laws of electromagnetism.

Ampere's Law:
Ampere's law relates the magnetic field surrounding a closed loop to the electric current passing through the loop. It states that the line integral of the magnetic field around a closed loop is equal to the total current passing through the loop.

Mathematical Representation:
Mathematically, Ampere's law can be expressed as:

∮B · dl = μ₀I

where B is the magnetic flux density, dl is an infinitesimal length element along the closed loop, μ₀ is the permeability of free space, and I is the total current passing through the loop.

Derivation:
Consider a closed loop in the form of a circle. The magnetic field intensity (H) can be defined as the magnetic field strength at the center of the loop. The magnetic flux density (B) can be considered as the magnetic field strength at any point on the loop.

According to Ampere's law, the line integral of B · dl around the loop is equal to the total current passing through the loop. Since the magnetic field is assumed to be constant along the loop, the integral simplifies to the product of B and the circumference of the loop.

B ∮dl = μ₀I

As the loop is a circle, the circumference can be expressed as 2πr, where r is the radius of the circle.

B(2πr) = μ₀I

Simplifying the equation, we get:

B = (μ₀I) / (2πr)

This equation clearly shows that the magnetic flux density (B) is directly proportional to the magnetic field intensity (H), which is represented by the current passing through the loop (I). The constant of proportionality is given by μ₀ / (2πr).

Therefore, the statement "The magnetic flux density is directly proportional to the magnetic field intensity" is true.