A long straight cylindrical wire of radius R carries a current I uniformly distributed over its cross-section. If the ratio of the magnetic field magnitude at a point 2 R from the axis to the magnet

Question

A long straight cylindrical wire of radius R carries a current I uniformly distributed over its cross-section. If the ratio of the magnetic field magnitude at a point 2 R ​ from the axis to the magnetic field magnitude at a point 2 R from the axis is N , find the value of N .

TestHub · Accepted Answer

For a point inside the wire ( r < R ), the magnetic field is given by B in ​ = 2 π R 2 μ 0 ​ I r ​ . At r = 2 R ​ , B 1 ​ = 2 π R 2 μ 0 ​ I ( R /2 ) ​ = 4 π R μ 0 ​ I ​ . For a point outside the wire ( r > R ), the magnetic field is given by B o u t ​ = 2 π r μ 0 ​ I ​ . At r = 2 R , B 2 ​ = 2 π ( 2 R ) μ 0 ​ I ​ = 4 π R μ 0 ​ I ​ . The ratio N = B 2 ​ B 1 ​ ​ = μ 0 ​ I / ( 4 π R ) μ 0 ​ I / ( 4 π R ) ​ = 1 .

Physics - Magnetism Question with Solution | TestHub

Doubts & Discussion

JEE Main 2027 (Class 12)