Question

The region inside a current carrying toroid is filled with a material (Niobium) having susceptibility \(χ = 2.6\times 10^{-5}\). The percentage increase in the magnetic field in the presence of Niobium over that without it, is

• A. \(2.6\times 10^{-5}\)
• B. \(2.6\times 10^{-4}\)
• C. \(2.6\times 10^{-3}\)
• D. \(2.6\times 10^2\)

Hint:

The field with a material is B = mu0 (1 + chi) n I.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Inside a toroid the field without a material is \(B_0 = \mu_0 nI\). With a material of susceptibility \(\chi\), the field becomes \(B = \mu_0(1 + \chi)nI = (1 + \chi)B_0\).

Step 2: Key Formula or Approach:
The fractional increase is \(\frac{B - B_0}{B_0} = \chi\).

Step 3: Detailed Explanation:
\[ \%\ \text{increase} = \chi \times 100 = 2.6 \times 10^{-5} \times 100 = 2.6 \times 10^{-3}\% \]
Option A, \(2.6 \times 10^{-5}\), is the fractional increase and has not been converted to a percentage.

Final Answer:
The increase is \(2.6 \times 10^{-3}\%\), option (C). \[ \boxed{2.6 \times 10^{-3}} \]