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 integral of the magnetic field around a closed loop is equal to the permeability of free space times the current passing through the loop.

Given:
Current density (J) = 5 A
Charge density (ρ) = 12j units in the positive y direction
z component is below the sheet

To calculate the magnetic field intensity, we can consider a rectangular Amperian loop with sides parallel to the sheet of current. The loop will enclose a current (I) passing through it, which is equal to the current density (J) multiplied by the area of the loop.

Let's consider a loop with sides of length 'a' in the x-direction and 'b' in the y-direction.

Calculating the current passing through the loop:
The charge density (ρ) is given in terms of units in the positive y direction. So, the area of the loop is a*b.

Current (I) = Current density (J) * Area of the loop
I = 5 A * a*b

Applying Ampere's law:
According to Ampere's law, the integral of the magnetic field (B) around the loop is equal to μ0 times the current (I) passing through the loop.

∮B.dl = μ0 * I

Since the magnetic field is constant in magnitude and direction along the loop, the integral simplifies to B * 2a + B * 2b = μ0 * I.

Simplifying the equation:
2aB + 2bB = μ0 * I

2(B * a + B * b) = μ0 * I

2(B * (a + b)) = μ0 * I

B * (a + b) = μ0 * I / 2

B = μ0 * I / (2 * (a + b))

Since the z component is below the sheet, the value of b is very large compared to a. Therefore, we can assume b >> a, and the equation becomes:

B ≈ μ0 * I / (2 * b)

Substituting the given values:
B = (4π × 10^-7 T·m/A) * (5 A) / (2 * b)
B = (2π × 10^-7 T·m) / b

As b approaches infinity, the magnetic field intensity (B) approaches zero.
Therefore, the correct answer is option 'b) 0'.