A surface current A/m flows on the surface z = 0, separating two media with magnetic permeabilities µ1 and µ2.

To find the magnitude of the normal component of the magnetic field, we need to consider the boundary conditions at the interface between the two media.

Boundary Conditions:
1. The tangential component of the magnetic field is continuous across the interface.
2. The normal component of the magnetic field has a discontinuity across the interface proportional to the surface current density.

Given:
- Magnetic field in region 1 = mT
- Magnetic permeability in region 1 = µ1
- Magnetic permeability in region 2 = µ2

Approach:
We will use these boundary conditions to find the normal component of the magnetic field at the interface.

Step 1: Find the Surface Current Density
The surface current density Js is related to the surface current I by the equation Js = I / Δl, where Δl is a small length along the current flow. Since we are given the surface current in A/m, we can directly use Js = A/m.

Step 2: Apply the Boundary Conditions
Let's consider a small Amperian loop just above the interface, enclosing a length Δl. The magnetic field B1 in region 1 is mT, and the magnetic field B2 in region 2 is unknown.

Using Ampere's circuital law, we can write the line integral of the magnetic field around the loop as:
∮ B.dl = µ0(I + I') --(1)

Where I is the current enclosed by the loop in region 1 and I' is the current enclosed by the loop in region 2.

For region 1:
The length of the loop is Δl, and the magnetic field is B1. So, the line integral is B1 * Δl.

For region 2:
The length of the loop is also Δl, but the magnetic field is B2. So, the line integral is B2 * Δl.

Substituting these values into equation (1), we get:
B1 * Δl + B2 * Δl = µ0(I + I')

Step 3: Find the Normal Component of the Magnetic Field
The normal component of the magnetic field is given by Bn = B2 - B1, as it is the difference between the magnetic fields in the two regions.

Substituting B2 - B1 for the line integral in equation (1), we get:
(B2 - B1) * Δl = µ0(I + I') - B1 * Δl

Simplifying the equation, we find:
Bn = (µ0 * (I + I') - B1 * Δl) / Δl

Since Δl is a small length, we can take the limit as Δl approaches zero:
Bn = µ0 * (I + I') - B1

Step 4: Find the Magnitude of the Normal Component of the Magnetic Field
To find the magnitude of Bn, we need to find the total current I' in region 2. Since the surface current density Js is given in A/m, we can calculate I' by multiplying Js by the length of the interface.

Let's