Question:
The susceptibility of Al is $2 \times 10^{-5}$. The percent increase in the magnetic field when the space within a current carrying toroid is filled with Al is:
The susceptibility of Al is $2 \times 10^{-5}$. The percent increase in the magnetic field when the space within a current carrying toroid is filled with Al is:
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Percent change in $B$ is simply susceptibility ($\chi$) multiplied by 100.
Updated On: May 12, 2026
- $2 \times 10^{-2}$
- $2 \times 10^{-3}$
- $2 \times 10^{-4}$
- $2 \times 10^{-5}$
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The Correct Option is B
Solution and Explanation
Step 1: Concept
The magnetic field $B$ inside a toroid filled with a medium is given by $B = \mu H$, where $\mu$ is the permeability of the medium. In a vacuum, the field is $B_0 = \mu_0 H$.
Step 2: Meaning
Relative permeability $\mu_r$ is related to magnetic susceptibility $\chi$ by the formula: $\mu_r = 1 + \chi$. The magnetic field in the medium is $B = \mu_r B_0 = (1 + \chi)B_0$.
Step 3: Analysis
The increase in the magnetic field is $\Delta B = B - B_0 = \chi B_0$. The fractional increase is $\frac{\Delta B}{B_0} = \chi$. To find the percent increase: $\text{Percent Increase} = \chi \times 100$.
Step 4: Conclusion
Given $\chi = 2 \times 10^{-5}$: $\text{Percent Increase} = (2 \times 10^{-5}) \times 100 = 2 \times 10^{-3}$. Final Answer: (B)
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