Magnetic Intensity Definition, Formula - Class 12 Magnetism and Matters

1. The magnetic field produced by the external source of current is called magnetising field.
2. The magnetising field depends on external free currents and geometry of current carrying conductor.
3. Magnetic intensity at a point in a magnetic field is defined as the number of magnetic lines of force passing normally per unit area about that point taken in free space in the absence of any substance.
4. In vacuum the ratio of magnetic induction $\left(\mathrm{B}_{0}\right)$ and magnetic permeability $\left(\mu_{0}\right)$ is called magnetising field H i.e. $H =\frac{ B _{0}}{\mu_{0}}$
5. In a toroidal solenoid the magnetic induction of field produced in material of Toroid is

$B=\mu n I$ so Magnetising field $H =\frac{ B }{\mu}= nI$

The magnetic intensity may be defined as the number of ampere turns flowing round a unit length of toroidal solenoid to produce that magnetic field in the solenoid.

In S$\mathbf{S} \mathbf{I}$ system $H =\frac{ B }{\mu}=\frac{\text { tesla }}{\text { tesla meter }- amp ^{-1}}=$ ampere-meter $^{-1}\left( Am ^{-1}\right)$

$H =\frac{ B _{0}}{\mu_{0}}=\frac{\frac{ F }{ q _{0} v }}{\mu_{0}}=\frac{ F }{ q _{0} v \mu_{0}}=\frac{ N }{ C \left( ms ^{-1}\right) TmA ^{-1}}= Nm ^{-2} T ^{-1}$

$H =\frac{ N }{ m ^{2} T }=\frac{ N }{ Wb }= NWb ^{-1}= Jm ^{-1} Wb ^{-1}$

In CGS System,  unit of H is oerested

• 1 oerested $=\frac{1 \text { gauss }}{\mu_{0}}=\frac{10^{-4} T }{4 \pi \times 10^{-7} TmA ^{-1}}=\frac{1000}{4 \pi} Am ^{-1}=80 Am ^{-1}$

(a) Solenoid $B =\mu_{0} nI$ H = n$\mathbf{I}$with $n=\frac{N}{L}$ = no. of turns per unit length.

(b) Toroid $B =\mu_{0} nI \quad H = nI$ with $n =\frac{ N }{2 \pi R }$

(c) Plane coil $B =\frac{\mu_{0} nI }{2 R } \quad H =\frac{ nI }{2 R }$

(d) Current carrying element $dB =\frac{\mu_{0} I \overrightarrow{ d \ell} \times \overrightarrow{ r }}{4 \pi r ^{3}}$ $dH =\frac{ I (\overrightarrow{ d }(\times \overrightarrow{ r })}{4 \pi r ^{3}}$

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