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=I3Current in smaller cylinder (if there were) : I2 = I+I3=4I3For  A:BA=Bwhole−cylinder−Bsmall−cylinder⇒ BA=0−μ0(I/3)2π(R/2)=−μ0I3πR For  B:BB=Bwhole−cylinder−Bsmall−cylinder=μ0(4I3)(R/2)2πR2−0=μ0I3πR .