The physical quantity with the unit J/T is magnetic field intensity.

Magnetic Field Intensity:
Magnetic field intensity (H) is a physical quantity that represents the strength of a magnetic field. It is defined as the force experienced by a unit magnetic pole placed in a magnetic field. The SI unit of magnetic field intensity is ampere per meter (A/m), but it can also be expressed in terms of joules per tesla (J/T).

Scalar or Vector Quantity:
Magnetic field intensity is a vector quantity because it has both magnitude and direction associated with it. The direction of the magnetic field intensity is defined by the direction of the force experienced by a positive test charge moving in the field. The magnitude of the magnetic field intensity represents the strength of the magnetic field.

Explanation:
To understand why magnetic field intensity is a vector quantity, let's consider the force experienced by a positive test charge moving in a magnetic field. According to the Lorentz force law, the force (F) experienced by a positive charge (q) moving with velocity (v) in a magnetic field (B) is given by the equation F = qvBsinθ, where θ is the angle between the velocity vector and the magnetic field vector.

From this equation, it is clear that the force experienced by the charge depends on the direction of the velocity vector, the magnetic field vector, and the angle between them. Therefore, the magnetic field intensity, which represents the force experienced by a unit magnetic pole, must also have a direction associated with it.

Representation:
In vector notation, the magnetic field intensity (H) is represented by a vector with both magnitude and direction. The magnitude of H is given by H = B/μ₀, where B is the magnetic flux density and μ₀ is the permeability of free space. The direction of H is perpendicular to the magnetic field lines and is defined by the right-hand rule.

To summarize, magnetic field intensity is a vector quantity represented by a vector with units of J/T. It has both magnitude and direction, representing the strength and orientation of the magnetic field.