JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Magnetic Properties of Matter

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The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility

χ_{m g} = 1.2 \times 1 0^{- 5}

) is:

(A) $\frac{6}{5} \times 1 0^{- 3} %$ ✓ Correct
(B) $\frac{5}{6} \times 1 0^{- 5} %$
(C) $\frac{5}{6} \times 1 0^{- 4} %$
(D) $\frac{5}{3} \times 1 0^{- 5} %$

Answer: (A)

Solution

Filling the solenoid with a medium of relative permeability

μ_{r} = 1 + χ

multiplies the field by

μ_{r}

, so the fractional increase is simply

χ

. As a percentage,

\frac{Δ B}{B} \times 100 = χ \times 100 = (1.2 \times 1 0^{- 5}) \times 100 = 1.2 \times 1 0^{- 3} %.

The percentage increase in the magnetic field is

\frac{6}{5} \times 1 0^{- 3} %

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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