Which of the following pairs has quantities of the same dimensions?
A. Magnetic field B and magnetizing field intensity H
B. Magnetic field B and intensity of magnetization I
C. Magnetizing field intensity H and intensity of magnetization I
D. Longitudinal strain and magnetic susceptibility.
The magnetic field B, magnetizing field intensity H and intensity of magnetization I are related by the formula
Here μ0 is the absolute permeability of vacuum having dimensional formula
We know that,
Same dimension substance are added and subtracted to give same dimensions. So that dimensions of magnetic field intensity H and intensity of magnetization I are same. Therefore option(c) is correct.
Since H and I are of same dimensions and H and B are of different dimensions, therefore dimensions of B and I are not same. therefore option(b) is incorrect.
Magnetic susceptibilityis given by formula
Where,
I=magnetization
H=magnetic intensity
Since dimensions of I and H are same so, χ is a dimensionless quantity.
Similarly, longitudinal strain is given by formula
Where,
Δl=change in length
l= length
hence, strain is also a dimensionless quantity
therefore option(d) is correct.
Therefore, H and I have same dimension and strain and susceptibility have same dimensions.