A rod with circular cross-section area 2 cm 2 and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0 . 4 A flows in the wire windings, the total magnetic flux produced inside windings is 4 π × 10 - 6 Wb . The relative permeability of the rod is (Given : Permeability of vacuum μ 0 = 4 π × 10 - 7 N A - 2 )

Step-by-step solution

Magnetic flux is given by ϕ = N B A , here, N is number of turns, B is magnetic field and A is area. Given here, ϕ = 4 π × 10 - 6   Wb ,   A = 2   cm 2 ,   N = 400 ,   I = 0 . 4   A . Putting the values, ϕ = 400 × μ r μ 0 n I × A ⇒ 4 π × 10 - 6   = 400 μ r × 4 π × 10 - 7 × 400 0 . 4 × 0 . 4 × 2 × 10 - 4 ⇒ μ r = 125