Q. Find the percentage increase in the magnetic field B when the space within the current carrying toroid is filled with aluminum. The susceptibility of aluminium is 2.1 × 10^{-5}

(a) 3.1 × 10^{-3}

(b) 1.1 × 10^{-3}

(c) 2.1 × 10^{-3}

(d) 2.1 × 10^{-5}

Ans: (c)

$ \displaystyle B_0 = \mu_0 H$ (Where H = n i)

$ \displaystyle B = \mu_0 \mu_r H$

$ \displaystyle B = \mu_0 (1 + \chi_m) H$

Percentage increase in magnetic field is

$ \displaystyle = \frac{B – B_0}{B_0}\times 100$

$ \displaystyle = \frac{\mu_0 \chi_m H}{\mu_0 H }\times 100$

$ \displaystyle = \chi_m \times 100 $

$ \displaystyle = 2.1 \times 10^{-5}\times 100 $

= 2.1 × 10^{-3}