Question

An infinite rod of a magnetic material with relative permittivity fur sits such that its axis is perpendicular to the direction of a uniform magnetic field in which it is immersed. The rod has a circular cross section, with radius . Find the magnetic field H inside and outside the rod. Sketch the field distribution. You may use results derived in lectures or problem sets, but justification must be provided.

Answer 1

Adjacent figure shows the direction of applied magnetic field and orientation of rod we know B vector = mu_0 (H vector + m vector) Always magnetized field direction is opposite to the applied field direction H vector = B vector/mu_0 - m vector H vector inside the rod: - H vector = B vector/mu_0 - m vector where m vector = Intensity of magnetization. H vector = B vector/mu = B vector/mu_0 mu_r H vector outside the rod: - m vector = 0 outside the rod H vector = B vector/mu_0 = B vector/mu_0 mu_r = B vector/mu_0 (mu_r = 1 for air) H vector is due to free currents, m vector is due to bound currents Hence Inside (or) outside H vector is same it does not Alters. Below figure shows the circular cross-section and applied field direction. B_in > B_out B - Inside and outside H_in = H_out H - Inside and and outside