To find the magnetic field intensity due to an infinite sheet of current, we can use Ampere's Law. Ampere's Law states that the line integral of the magnetic field around a closed loop is equal to the product of the current enclosed by the loop and the permeability of free space (μ0).

Given:
Current density (J) = 5 A
Charge density (ρ) = 12 j units
z-component of the field above the sheet

Let's calculate the magnetic field intensity step by step:

1. Determine the current enclosed by a closed loop above the sheet:
Since the sheet is infinite, the entire current is enclosed by any closed loop above the sheet. Therefore, the current enclosed is equal to the total current (J) = 5 A.

2. Determine the direction of the magnetic field:
The magnetic field due to an infinite sheet of current is perpendicular to the sheet and follows the right-hand rule. In this case, the magnetic field will be in the negative x-direction.

3. Determine the shape of the closed loop:
Since the magnetic field is in the negative x-direction, we can choose a rectangular loop with sides parallel to the y and z axes. The loop will have a height (h) in the y-direction and a width (w) in the z-direction.

4. Calculate the line integral of the magnetic field around the closed loop:
The line integral of the magnetic field along the sides parallel to the y-axis will be zero since the magnetic field is perpendicular to these sides. Therefore, we only need to calculate the line integral along the sides parallel to the z-axis.

Using Ampere's Law, the line integral of the magnetic field along these sides is given by:
∮ B · dl = μ0 * Ienclosed

The left-hand side of the equation is the product of the magnetic field (B) and the length (w) of the sides parallel to the z-axis. The right-hand side is the product of the permeability of free space (μ0) and the current enclosed (Ienclosed).

5. Calculate the magnetic field intensity:
Since the line integral along the sides parallel to the y-axis is zero, we can write the equation as:
B * w + B * w = μ0 * Ienclosed

Simplifying the equation, we get:
2Bw = μ0 * Ienclosed

Solving for B, we have:
B = μ0 * Ienclosed / (2w)

Since the z-component of the field is above the sheet, we can take the width (w) to be infinitesimally small, approaching zero. In this case, the magnetic field intensity becomes:
B = μ0 * Ienclosed / (2 * 0) = ∞

Therefore, the magnetic field intensity due to an infinite sheet of current with a charge density of 12 j units and the z component above the sheet is infinite.