The correct statement given below are:(A) X = 1 + μ_r (B) μ_r = 1 + X…

The correct answer is Option (3) → (B), (C) and (E) only

In a magnetic material the total field is B = \( B_0 \) (the field of the current alone, \( B_0 = \mu_0 H \)) plus the field of the magnetisation M. The magnetic susceptibility \( \chi \) (written X in the question) is defined by \( M = \chi H \).

(A) \( X = 1 + \mu_r \) — Incorrect. From \( B = \mu_0(H + M) = \mu_0(1+\chi)H = \mu_0\mu_rH \) we get \( \mu_r = 1 + \chi \), so \( \chi = \mu_r - 1 \).

(B) \( \mu_r = 1 + X \) — Correct. This is the relation just found.

(C) \( B = \mu_0(H + M) \) — Correct. This is the definition of the magnetic intensity H, since \( H = B/\mu_0 - M \).

(D) \( H = B_0\mu_0 \) — Incorrect. H is \( B_0/\mu_0 \); \( \mu_0 \) belongs in the denominator.

(E) \( B_0 = \mu_0 H \) — Correct. For a solenoid the field due to the current alone is \( B_0 = \mu_0 nI \) and \( H = nI \).

NCERT (2026-27):
Summary – “… 5. Consider a material placed in an external magnetic field \( \mathbf{B}_0 \). The magnetic intensity is defined as,

    \( \displaystyle \mathbf{H} = \frac{\mathbf{B}_0}{\mu_0} \)

The magnetisation M of the material is its dipole moment per unit volume. The magnetic field B in the material is,

    \( \displaystyle \mathbf{B} = \mu_0\left(\mathbf{H} + \mathbf{M}\right) \)”

Summary – “… 6. For a linear material \( \mathbf{M} = \chi\mathbf{H} \). So that \( \mathbf{B} = \mu\mathbf{H} \) and \( \chi \) is called the magnetic susceptibility of the material. The three quantities, \( \chi \), the relative magnetic permeability \( \mu_r \), and the magnetic permeability \( \mu \) are related as follows:

    \( \displaystyle \mu = \mu_0\mu_r \qquad \mu_r = 1 + \chi \)”