The magnetic field intensity inside a toroid can be determined using 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 permeability of free space (μ0) and the total current passing through the loop.

Ampere's Law:
∮B · dl = μ0 · I_enclosed

where B represents the magnetic field, dl is an infinitesimal vector element along the closed loop, μ0 is the permeability of free space (4π × 10^-7 T·m/A), and I_enclosed is the current enclosed by the loop.

In the case of a toroid, the magnetic field is concentrated inside the toroid due to the arrangement of the current-carrying wire. The wire is wound in a circular loop, creating a magnetic field that is primarily confined within the toroid.

Calculating the Magnetic Field Intensity:

To calculate the magnetic field intensity inside the toroid, we need to determine the current enclosed by a closed loop within the toroid.

Given:
Number of turns per meter (N) = 3000 turns/m
Radius of the toroid (r) = 2 cm = 0.02 m
Current passing through the toroid (I) = 5 A

Step 1: Determine the total current enclosed by the loop.
The total current enclosed by the loop can be calculated by multiplying the number of turns per meter by the current passing through the toroid.

Total current enclosed (I_enclosed) = N × I

Substituting the given values:
I_enclosed = 3000 turns/m × 5 A = 15000 A

Step 2: Calculate the magnetic field intensity inside the toroid using Ampere's Law.
The magnetic field intensity (B) inside the toroid can be determined by rearranging Ampere's Law.

B = (μ0 · I_enclosed) / (2π · r)

Substituting the values:
B = (4π × 10^-7 T·m/A) × (15000 A) / (2π × 0.02 m)

Simplifying the expression:
B = (2 × 10^-7 T·m/A) × (15000 A) / (0.04 m)

B = 3 × 10^-5 T

Therefore, the magnitude of the magnetic field intensity in the interior of the toroid is 3 × 10^-5 Tesla.