Magnetic Field Intensity in the Interior of a Toroid

To determine the magnitude of the magnetic field intensity in the interior of the toroid, we can use Ampere's Law. Ampere's Law states that the line integral of the magnetic field along a closed path is equal to the product of the current enclosed by the path and the permeability of free space.

Step 1: Determine the Current Enclosed by the Path
The toroid is carrying a current of 5A. Since the entire current passes through each turn of the toroid, the current enclosed by the path is equal to the total current, which is 5A.

Step 2: Determine the Path
The path we consider is a circular path inside the toroid, coaxial with the turns of the toroid. The radius of the path is the radius of the toroid, which is 2cm or 0.02m.

Step 3: Determine the Permeability of Free Space
The permeability of free space, denoted by μ₀, is a constant equal to 4π × 10⁻⁷ Tm/A.

Step 4: Apply Ampere's Law
Applying Ampere's Law, we have:

∮ B · dl = μ₀I_enclosed

Here, B is the magnetic field intensity, dl is an infinitesimal vector element along the path, and ∮ represents the line integral along the closed path.

Step 5: Calculate the Magnetic Field Intensity
The line integral of B · dl can be simplified to B × 2πr, where r is the radius of the path. Substituting the known values, we have:

B × 2π × 0.02 = (4π × 10⁻⁷) × 5

Simplifying the equation, we find:

B = (4π × 10⁻⁷ × 5) / (2π × 0.02)

B = 10⁻⁶ T

Therefore, the magnitude of the magnetic field intensity in the interior of the toroid is 10⁻⁶ Tesla.