A long solid cylindrical conductor of radius R has current density J=J₀r². Determine (field at R/2)/(field at R), where field at R is the field at the surface.
Physics · Magnetic effect of current · ampere's law and its application
JEE Mains NEET

Question

A long solid cylindrical conductor of radius R has current density J=J₀r². Determine (field at R/2)/(field at R), where field at R is the field at the surface.

G1 Physics · Accepted Answer

Inside, B∝r³. Therefore (field at R/2)/(field at R)=(1/2)³=1/8=0.125.