JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Magnetic Properties of Matter

The free space inside a current carrying toroid is filled with a material of susceptibility

2 \times 1 0^{- 2}

. The percentage increase in the value of magnetic field inside the toroid will be

(A) $2%$ ✓ Correct
(B) $0.2%$
(C) $0.1%$
(D) $1%$

Answer: (A)

Solution

Filling the core with a material of susceptibility

χ_{m}

raises the field by the factor

μ_{r} = 1 + χ_{m}

, since

B = μ_{r} B_{0}

. The fractional increase is

\frac{B - B _{0}}{B _{0}} = χ_{m}

. With

χ_{m} = 2 \times 1 0^{- 2}

the field increases by

2 \times 1 0^{- 2} \times 100 = 2%

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option

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