Q4. Assertion: the relative magnetic permeability of a material plays the part that the dielectric constant plays in electrostatics. Reason: just as ε = Kε, the permeability is μ = μrμ. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: μr multiplies the vacuum constant μ as K multiplies ε (NCERT page 146).
Q5. A thin toroid, approximated by its mean circular path and negligible leakage, has 3500 turns per metre along that path and carries 2.0 A, and its iron core gives B = 1.2 T. Find H, M, μr and χ.
H = nI = 3500 × 2.0 = 7.0 × 10 A/m. M = B/μ − H = 1.2/(4π × 10−7) − 7.0 × 10 ≈ 9.5 × 105 A/m. μr = B/(μH) ≈ 136, so χ = μr − 1 ≈ 135 (NCERT Eqs. (5.11)–(5.15), page 146). This χ holds only at this field, since iron is not linear.
Q6. Show that H and M have the same dimensions as each other, and find them.
M is magnetic moment (A m) per volume (m), so A m−1, dimensions [L−1 A]. H = B/μ − M must have the same dimensions as M, and B/μ = T/(T m A−1) = A m−1 agrees (NCERT pages 145–146).
Q7. In NCERT Example 5.5, why does the magnetising current come out as 798 A when worked exactly but 794 A in NCERT’s solution?
Exactly, μn(I + IM) = μrμnI gives IM = (μr − 1)I = 399 × 2 = 798 A. NCERT uses the rounded value B = 1 T in place of B = 1.005 T, which gives 794 A (NCERT page 147).