Physics · Magnetism And Matter · NEET
The dimensionless relation is mu_r = 1 + chi. Both mu_r (relative permeability) and chi (susceptibility) are pure numbers with no units, so they can be added directly. The absolute permeability mu is NOT 1 + chi — it carries units. To get mu you multiply by mu_0: mu = mu_0 * mu_r = mu_0 * (1 + chi). A common NEET slip is writing mu = 1 + chi; that mixes a unitless number with a quantity that has units of T m/A.
mu is the absolute (or total) permeability of the material, measured in tesla-metre per ampere (T m/A), same units as mu_0. mu_r is the relative permeability, a pure number that tells you how many times better the material lets magnetic field through compared to vacuum. They are connected by mu = mu_0 * mu_r. For vacuum mu_r = 1, so mu = mu_0 = 4*pi*10^-7 T m/A.
It comes from the NCERT chain of definitions. Inside a material, B = mu_0 * (H + M). Since magnetisation M = chi * H, we get B = mu_0 * (H + chi*H) = mu_0 * (1 + chi) * H. Comparing this with B = mu * H shows mu = mu_0 * (1 + chi). So the mu_0 is the leftover factor from the definition B = mu_0(H + M); it is not something you add on separately.
Use mu_r = 1 + chi. Diamagnetic: chi is small and negative (like -10^-5), so mu_r is slightly less than 1. Paramagnetic: chi is small and positive (like +10^-5), so mu_r is slightly more than 1. Ferromagnetic: chi is large and positive (hundreds to thousands), so mu_r is very large (like 400 or more, as in NCERT Example 5.5).
M = chi * H defines susceptibility (magnetisation per unit magnetic intensity). Then B = mu_0(H + M) = mu_0(1 + chi)H = mu_0 * mu_r * H = mu * H. So all three quantities B, H, M feed into the single relation mu = mu_0(1 + chi). Only ONE of chi, mu_r, mu is independent — give one and you can find the other two.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The relative permeability equals one plus the susceptibility: mu_r = 1 + chi. In terms of absolute permeability, mu = mu_0 * mu_r = mu_0 * (1 + chi), where mu_0 = 4*pi*10^-7 T m/A is the permeability of free space.
Yes, the relation mu_r = 1 + chi holds for diamagnetic, paramagnetic and (linear-region) ferromagnetic materials. For ferromagnets, chi and mu_r are not constant because M is not simply proportional to H, but the definition mu_r = 1 + chi still connects the instantaneous values.
For vacuum (free space) chi = 0, so mu_r = 1 + 0 = 1 and mu = mu_0. This is the reference against which all materials are compared.
Rearrange mu_r = 1 + chi to chi = mu_r - 1 = 400 - 1 = 399. Such a large positive susceptibility means the material is ferromagnetic (this is the NCERT Example 5.5 solenoid core).
Only one is independent. Because mu_r = 1 + chi and mu = mu_0 * mu_r, giving any one of chi, mu_r or mu lets you calculate the other two, as stated in NCERT.
