JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Magnetic Properties of Matter

The value of aluminium susceptibility is

2.2 \times 1 0^{- 5}

. The percentage increase in the magnetic field if space within a current carrying toroid is filled with Aluminium is

\frac{x}{1 0 ^{4}}

. Then the value of x is ____.

Answer: 22

Solution

Filling the core raises the field from

B_{0}

B = μ_{r} B_{0} = (1 + χ) B_{0}

, so the fractional increase is the susceptibility itself. As a percentage,

\frac{B - B _{0}}{B _{0}} \times 100 = χ \times 100 = 2.2 \times 1 0^{- 5} \times 100 = 2.2 \times 1 0^{- 3}

Written as

\frac{x}{1 0 ^{4}}

this percentage gives

x = 22

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Integer answer

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