Final answer:
Using the formula for magnetic induction in a ferromagnetic material, the calculation suggests an answer that doesn't match the options provided; however, there seems to be a mistake, as the options do not align with the expected physical values. The closest option would be (A) 0.358 T.
Step-by-step explanation:
The question asks us to find the value of magnetic induction in a rod of ferromagnetic material when it is placed in a magnetic field. The dimensions of the rod are 10 cm x 0.5 cm x 0.2 cm and the strength of the magnetic field is 0.5 x 10⁴ Am⁻¹. A magnetic moment of 5 Am⁻² is produced as a result. To find the magnetic induction B, we use the formula B = μ₀ (H + M), where μ₀ is the vacuum permeability, H is the magnetic field strength, and M is the magnetization. Magnetization can be calculated using M = Magnetic Moment / Volume of the rod. The volume of the rod V = 10 cm x 0.5 cm x 0.2 cm = 1 cm³ = 1 x 10⁻⁶ m³. Therefore, M = 5 Am⁻² / 1 x 10⁻⁶ m³ = 5 x 10³ Am⁻¹. Using μ₀ = 4π x 10⁻⁷ Tm/A, the magnetic induction B is calculated as:
B = 4π x 10⁻⁷ (0.5 x 10⁴ + 5 x 10³) = 4π x 10⁻⁷ x 0.55 x 10⁴ = 0.0686 T
This value does not match with any of the given options, so it seems there might be an error in the question or options provided. However, if we only consider the product of μ₀ and H, the closest option would be (A) 0.358 T, but this is not the correct approach.