From a cylinder of radius R, a cylinder of radius R/2 is removed, as shown in figure. Current flowing in the remaining cylinder is I. Then, magnetic field strength is:

Current density: ρ=IπR2-π(R/2)2⇒ρ=4I3πR2 Current in smaller cylinder (if there were):I1=ρπR22=I3  For A:BA=Bwhole-cylinder -Bsmall-cylinder  ⇒  BA=0-μ0(I/3)2π(R/2)=-μ0I3πR  For B:BB=Bwhole-cylinder -Bsmall oylinder  =μ0(I+I/3)(R/2)2πR2-0=μ0I3πR