Calculation of Magnetic Flux Density

To find the magnetic flux density at a point due to a finite current length element, we can use the Biot-Savart law. The Biot-Savart law states that the magnetic field produced by a current-carrying conductor at a point is directly proportional to the current and inversely proportional to the distance from the conductor.

Given Data:
- Current in the element, I = 0.5 A
- Radius of the element, r = 100 nm = 100 × 10^(-9) m

Biot-Savart Law:
The magnetic field at a point P due to a small length element dl carrying current I can be calculated using the Biot-Savart law as follows:

dB = (μ₀ / 4π) * (I * dl × r̂) / r²

Where:
- dB is the magnetic field produced by the small length element
- μ₀ is the permeability of free space (4π × 10^(-7) T·m/A)
- I is the current in the small length element
- dl is the vector representing the small length element
- r̂ is the unit vector pointing from the small length element to the point P
- r is the distance from the small length element to point P

Calculation:
In this case, we have a finite length element, so we need to consider the contribution of each small length element along the entire length.

Let's assume the length of the finite element is L. The magnetic field dB at a point P due to a small length element dl can be written as:

dB = (μ₀ / 4π) * (I * dl × r̂) / r²

The total magnetic field B at point P due to the entire finite length element can be found by integrating over the length of the element:

B = ∫ dB

Since the length of the element is finite, the magnetic field at point P will not be zero.

Therefore, the correct answer is option 'C' - 1.