A bar magnet of length `1cm` and cross-sectonal area `1.0 cm^2` produces a magnetic field of `1.5 xx 10^(-4) T` at a point in end-on position at a distance 15cm away from the centre. (a) Find the magnetic moment `M` of the magnet. (b) Find the magnetization `I` of the magnet. (c) Find the magnetic field `B` at the centre of the magnet.

Explanation

Given `d=15cm =0.15m`
`l=l cm =0.01m `
`A=1.0 cm^2 1xx10^(-4) m^2`
`B-=1.5xx10^(-4)T`
`We know vecB=(mu_0)/(4 pi)xx(2Md)/((d^2-l^2)^2)`
` implies 1.5xx10^(-4)=(10^(-7)xx2xx Mxx0.15)/((0.0225-0.000)^2)`
`=(3xx10^(-8)M)/(5.01xx10^(-4))`
` implies M=(1.5xx10^(-4))/(3xx10^(-8))`
`=2.5A.`
`(b) Magenatization I =M/V`
`=(2.5)/(10^(-4)xx10^(-2))`
`=(2.5xx10^6)A//m`
`(c) H=(M)/(4 pi l d^2)`
`=(4xx3.14xx0.01xx(0.15)^2)`
`2.5/(4xx3.14xx1xx10^(-2)xx225xx10^(-2))`
`Net H=H_N+ H_S`
`=2xx884.6xx10^(2)`
`=314 T`
` vecB=(mu_0)(-H+1)`
`-pixx10^(-7)(2.5xx10^(6)-2xx884.6)`
`=3.14T`.