A long straight metal rod has a very long hole of radius ‘a’ drilled parallel to the rod axis as shown in the figure. If the rod carries a current ‘i’, the value of magnetic induction on the axis of the hole will be, where OC = c

Question

G1 Physics · Accepted Answer

Use superposition of a full uniformly current-filled cylinder of radius b and a negative-current cylinder of radius a whose axis is displaced by c. Inside a uniformly current-filled cylinder B⃗=(μ₀J/2) ẑ×r⃗. At the cavity axis the r-dependent terms cancel, leaving B=μ₀Jc/2. With J=i/[π(b²-a²)], B=μ₀ic/[2π(b²-a²)]. Hence B.