A cylindrical cavity of diameter a exists inside a cylinder of diameter 2 a as shown in the figure. Both the cylinder and the cavity are infinity long. A uniform current density J flows along the leng

Question

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2 a as shown in the figure. Both the cylinder and the cavity are infinity long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by 12 N ​ μ 0 ​ a J , then the value of N is

TestHub · Accepted Answer

Current density J = area current ​ = A I ​ ⇒ I = JA Magnetic field B R ​ after removing cavity ( C ) B R ​ = B total ​ − B cavity ​ 2 πa μ 0 ​ I t ​ ​ − 2 π ( 2 3 ​ a ) μ 0 ​ I c ​ ​ = πa μ 0 ​ ​ [ 2 I t ​ ​ − 3 I c ​ ​ ] ( here I t ​ = J ( π a 2 ) I c ​ = J ( 4 π a 2 ​ ) ) = πa μ 0 ​ ​ [ 2 π a 2 J ​ − 12 π a 2 J ​ ] or, B R ​ = 12 5 μ 0 ​ a J ​ ​ Comparing it with 12 N ​ μ 0 ​ a J We get N = 5

Physics - Magnetism Question with Solution | TestHub

Doubts & Discussion