A permanent magnet in the shape of a thin cylinder of length `10cm` has `M=10^6A//m`. Calculate the magnetisation current `I_M`. (Here M is the intensity of magnetisation).

Explanation

Magnetization current is the additional current that needs to be passed through the magnet in the absence of the core that would give us the value of B as in the presence of core.
Given, intensity of magnetization, `M = 10^6` A/m
Length of the cylinder, 1 = 10 cm = 0.1 m
`B = mu_0 mu_r H = mu_0 r_1 (I + I_M) ) ` ...(i)
where I is the current flowing through the magnet.
Here, n = N/L
Here, N=1
`rArr n = 1/l`
from (i) `B = mu_0 mu_r H = (mu_0)/(l) (I + I_M) ` .....(ii)
also `I_m = (mu_r - 1) H`
Or ` H = (I_m)/((mu_r - 1))`
Since, the magnet is permanent, `mu_r gt gt 1`
` therefore H = (I_m)/(mu_r)`
from (ii)
`B =mu_0 mu_r (I_m)/(mu_r) = (mu_0)/(l) ( I+I_m)`
`B = mu_0 I_m = (mu_0)/(l) (I + I_m)`
Multiplying the whole equation with l, we get
` Bl = mu I_m l = mu_0 (I+ I_m) `
` rArr I_m l = mu_0 ( I + I_m)`
here I = 0
`rArr I_M = I_(m) l = 10^6 xx 0.1 = 10^5 A`