Question

The dimensional formula for intensity of magnetising field and magnetic susceptibility are.

• A. $\left[M^{0}A{L}^{-1}{T}^0\right]\left[M^0{A}^0{L}^0{T}^0\right]$
• B. $\left[M^0{A}^2{L}^{-1}{T}^2\right]\left[M^{0}AL{T}^{-1}\right]$
• C. $\left[M^0{A}^1{L}^{-1}{T}^2\right]\left[M^0{A}^0{L}^0{T}^0\right]$
• D. $\left[ML{T}^{-2}\right]\left[M{L}^2{T}^{-2}\right]$

Answer 1

Answer: (A)

Determining the dimensional formula for intensity of magnetising field:

The intensity of the magnetising field(H) is given by;

$H=\frac{B}{{\mu }_0}$

Where, ${\mu }_0$ is the permeability of free space and B is the magnetic field.

The dimension of the magnetic field is given by,

$F=iBl\sin \theta$

$Fordimension;$

$B=\frac{Force}{iL}$

$(\sin \theta hasnodimension.)$

Therefore the dimension of B is;

$DimensionofB=\frac{DimensionofF}{Dimensiionofi\times Diemnsionofl}$

$DimensionofB=\frac{\left[ML{T}^{-2}\right]}{\left[A\right]\left[L\right]}$

$DimensionofB=\left[M{A}^{-1}{T}^{-2}\right]$

The dimension of ${\mu }_0$ is gievn as, $\left[ML{A}^{-2}{T}^{-2}\right]$.

Now,

The dimension of H will be given as,

$DimensionofH=\frac{DiemsnionofB}{Diemsionof{\mu }_0}$

$DimensionofH=\frac{\left[M{A}^{-1}{T}^{-2}\right]}{\left[ML{A}^{-2}{T}^{-2}\right]}$

$DimensionofH=\left[M^0{L}^{-1}{A}^1{T}^0\right]$

Determining the dimensional formula of magnetic susceptibility:

Magnetic susceptibility(χ) is given as;

$\text{χ}=MH$

Here,

χ is a dimensionless quantity.

Thus,

The dimension of the intensity of the magnetising field is $\left[M^0{L}^{-1}{A}^1{T}^0\right]$ and susceptibility is a dimensionless quantity.

Thus,

Option B) $\left[M^0{L}^{-1}{A}^1{T}^0\right]$ and $\left[M^0{L}^0{A}^0{T}^0\right]$ is the correct option.