Question:
The space within the current carrying toroid is filled with aluminium of susceptibility \( \chi \). The percentage increase in the magnetic field \( B \) will be
The space within the current carrying toroid is filled with aluminium of susceptibility \( \chi \). The percentage increase in the magnetic field \( B \) will be
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The field inside a toroid with a core is multiplied by the relative permeability, which is one plus the susceptibility.
Updated On: Nov 13, 2026
- \( \frac{3}{2} \times 100 \)
- \( 2\chi \times 100 \)
- \( (1 + \chi) \times 100 \)
- \( \chi \times 100 \)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Without a core, \(B_0 = \mu_0 n I\). With a core of relative permeability \(\mu_r\), \(B = \mu_r B_0\), and \(\mu_r = 1 + \chi\).
Step 2: Increase in Field
\(B - B_0 = (1 + \chi)B_0 - B_0 = \chi B_0\).
Step 3: Percentage Increase
\(\dfrac{B - B_0}{B_0} \times 100 = \chi \times 100\).
Step 4: Compare the options
The percentage increase is \(\chi \times 100\), the last option.
Final Answer:
The percentage increase in the field is chi times 100. \[ \boxed{\text{(D) }\chi \times 100} \]
Without a core, \(B_0 = \mu_0 n I\). With a core of relative permeability \(\mu_r\), \(B = \mu_r B_0\), and \(\mu_r = 1 + \chi\).
Step 2: Increase in Field
\(B - B_0 = (1 + \chi)B_0 - B_0 = \chi B_0\).
Step 3: Percentage Increase
\(\dfrac{B - B_0}{B_0} \times 100 = \chi \times 100\).
Step 4: Compare the options
The percentage increase is \(\chi \times 100\), the last option.
Final Answer:
The percentage increase in the field is chi times 100. \[ \boxed{\text{(D) }\chi \times 100} \]
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