Question

The free space inside a current carrying toroid is filled with a material of susceptibility \( 2 \times 10^3 \). The percentage increase in the value of magnetic field inside the toroid will be:

• A. 0.2%
• B. 1%
• C. 2%
• D. 0.1%

Hint:

The susceptibility of a material increases the magnetic field inside a toroid by the factor \( (1 + \chi) \), where \( \chi \) is the susceptibility.

Answer 1

The Correct Option is C

We know the formula for the magnetic field inside a toroid is: \[ B = \frac{\mu_0 N I}{2 \pi r} \] Where \( \mu_0 \) is the permeability of free space and \( N \) is the number of turns. When a material with susceptibility \( \chi \) is added, the magnetic field increases by the factor: \[ B_{\text{new}} = B_0 (1 + \chi) \] Given that \( \chi = 2 \times 10^3 \), the percentage increase in the magnetic field is: \[ \text{Percentage increase} = \left( \frac{B_{\text{new}} - B_0}{B_0} \right) \times 100 = 2\% \] Thus, the correct answer is 2%.