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