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Magnetic Properties of Matter question

2023 · 11 Apr · Shift 1 · Q62
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  5. /2023 · 11 Apr · Shift 1 · Q62

Magnetic Properties of Matter question

2023 · 11 Apr · Shift 1 · Q62

JEE MainPhysicsMagnetic Properties of MatterMCQ+4 / −1
The free space inside a current carrying toroid is filled with a material of susceptibility 2×10−22 \times 10^{-2}2×10−2. The percentage increase in the value of magnetic field inside the toroid will be
  1. A
    0.1%
  2. B
    1%
  3. C
    2%
  4. D
    0.2%
View written solutionFree

Correct answer: C

  1. Magnetic field inside an air-core toroid

For a toroid, the magnetic field intensity is

H=NI2πrH = \frac{NI}{2\pi r}H=2πrNI​

where NNN is the number of turns, III is the current, and rrr is the mean radius.

Without magnetic material, the magnetic field is

B0=μ0HB_0 = \mu_0 HB0​=μ0​H

  1. When a material of susceptibility χ\chiχ is inserted

The permeability becomes

μ=μ0(1+χ)\mu = \mu_0(1+\chi)μ=μ0​(1+χ)

Hence the new magnetic field is

B=μH=μ0(1+χ)H=B0(1+χ)B = \mu H = \mu_0(1+\chi)H = B_0(1+\chi)B=μH=μ0​(1+χ)H=B0​(1+χ)

  1. Increase in magnetic field

The increase is

ΔB=B−B0=B0χ\Delta B = B - B_0 = B_0\chiΔB=B−B0​=B0​χ

So the fractional increase is

ΔBB0=χ\frac{\Delta B}{B_0} = \chiB0​ΔB​=χ

Given

χ=2×10−2=0.02\chi = 2\times 10^{-2} = 0.02χ=2×10−2=0.02

Therefore, percentage increase is

0.02×100=2%0.02 \times 100 = 2\%0.02×100=2%

  1. Option check
  • A: 0.1%0.1\%0.1% ❌
  • B: 1%1\%1% ❌
  • C: 2%2\%2% ✅
  • D: 0.2%0.2\%0.2% ❌

So the correct option is C.

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