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Magnetic Properties of Matter question

2022 · 28 Jun · Shift 2 · Q61
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  5. /2022 · 28 Jun · Shift 2 · Q61

Magnetic Properties of Matter question

2022 · 28 Jun · Shift 2 · Q61

JEE MainPhysicsMagnetic Properties of MatterMCQ+4 / −1
The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 ×\times× 10 −-− 5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?
  1. A
    1.2 ×\times× 10 −-− 5
  2. B
    1.2 ×\times× 10 −-− 3
  3. C
    1.8 ×\times× 10 −-− 3
  4. D
    2.4 ×\times× 10 −-− 5
View written solutionFree

Correct answer: A

  1. Magnetic field inside a solenoid

    For a long solenoid, B=μnIB = \mu n IB=μnI where μ\muμ is the permeability of the medium.

  2. Permeability in terms of susceptibility

    For a magnetic material, μ=μ0(1+χm)\mu = \mu_0(1+\chi_m)μ=μ0​(1+χm​) where χm\chi_mχm​ is the magnetic susceptibility.

    Given: χm=1.2×10−5\chi_m = 1.2 \times 10^{-5}χm​=1.2×10−5

  3. Field with air and with magnetic material

    • With air inside: Bair=μ0nIB_{\text{air}} = \mu_0 n IBair​=μ0​nI

    • With magnetic material inside: Bmat=μ0(1+χm)nIB_{\text{mat}} = \mu_0(1+\chi_m)nIBmat​=μ0​(1+χm​)nI

  4. Fractional increase in magnetic field

    Fractional increase is Bmat−BairBair\frac{B_{\text{mat}} - B_{\text{air}}}{B_{\text{air}}}Bair​Bmat​−Bair​​

    Substituting: μ0(1+χm)nI−μ0nIμ0nI=χm\frac{\mu_0(1+\chi_m)nI - \mu_0 nI}{\mu_0 nI} = \chi_mμ0​nIμ0​(1+χm​)nI−μ0​nI​=χm​

    Therefore, fractional increase=1.2×10−5\text{fractional increase} = 1.2 \times 10^{-5}fractional increase=1.2×10−5

  5. Option matching

    1.2×10−51.2 \times 10^{-5}1.2×10−5 corresponds to Option A.

Final Answer: A

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