Question

The magnetic field inside a long solenoid having 50 turns $c{m}^{-1}$ is increased from 2.5 $\times {10}^{-3}$T to 2.5 T when an iron core of cross-sectional area 4 $c{m}^2$ is inserted into it. Find (a) the current in the solenoid, (b) the magnetization I of the core and (c) the Pole strength developed in the core.

Answer 1

Here $B_1=2.5\times {10}^{-3}$ T

B_2 = 2.5 T

A = $4\times {10}^{-4}{m}^2$,

n = 50 turns/cm

= 5000 turns/m

(a) 2.5 $\times {10}^{-3}=4\pi \times {10}^{-7}\times 5000\times$ i

$\Rightarrow i=\frac{2.5\times {10}^{-3}}{4\pi \times {10}^{-7}\times 5000}$

= 0.398A = 0.4 A

(b) I = $\frac{B_2}{{\mu }_0}$ H

= $\frac{2.5\times {10}^{-3}}{4\pi \times {10}^{-7}}.(B_2-B_1)$

= $\frac{2.5\times 2.5(1-\frac{1}{1000})}{4\pi \times {10}^{-7}}$

$\approx 2\times 0^6$ A/m

(c) l = $\frac{M}{V}$

$\Rightarrow l=\frac{MI}{AI}=\frac{m}{A}$

$\Rightarrow$ m = lA

= $2\times {10}^6\times 4\times {10}^{-4}$

= 800 A-m.