The region inside a current carrying toroid winding has magnetic field ' B_0 | PGMN Solutions

The region inside a current carrying toroid winding has magnetic field ' B_0 '. If the region inside toroid winding is filled with platinum, the magnetic field becomes ' B '. What is percentage change in magnetic field?
[Susceptibility ' χ ' of platinum =2.9×〖10〗^(-4) ]
(A) 0.00029%
(B) 0.0029%
(C) 0.029%
(D) 0.29%
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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Magnetic Field due to Electric Current
📌 Topic: Magnetic Field in Magnetic Materials

🔹 Step 1: Introduce the core concept related to the question
When a magnetic material is placed in a magnetic field, the total magnetic field inside the material becomes slightly stronger or weaker depending on whether the material is paramagnetic or diamagnetic. This change is characterized by the magnetic susceptibility (χ) of the material.

🔹 Step 2: Explain how the concept applies to the given situation
Here, the toroid initially had magnetic field B₀ in air (or vacuum).
When platinum is introduced inside the toroid, the magnetic field becomes B.
Since platinum is a paramagnetic material, it slightly increases the magnetic field inside.

🔹 Step 3: Break down the logical steps required to solve the problem
The magnetic field B inside a material is related to the original field B₀ by a factor of (1 + χ) where χ is the susceptibility.
So, the field increases by a fraction equal to χ.

Thus, the percentage change in the magnetic field is simply: 👉 χ × 100
= 2.9 × 10⁻⁴ × 100
= 0.029%

🔹 Step 4: Explain the final theoretical conclusion
The magnetic field inside the toroid increases slightly due to the paramagnetic nature of platinum, and the percentage increase is directly determined by its susceptibility.

✅ Final Answer: (C) 0.029% 🚀

🔥 Pro Tip: For small values of magnetic susceptibility (as in weak paramagnetics like platinum), the percentage increase in magnetic field is approximately equal to χ × 100. No complicated steps needed! 🧲💡
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