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JEE Advanced2012PhysicsMagnetic Effects of CurrentActual

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 N 12 ₀ a J , then the value of N is

Correct answer

0

Step-by-step solution

Current density J= current area = I A I= JA Magnetic field B _ R after removing cavity ( C ) B _ R = B _ total - B _ cavity array l ₀ I_ t 2 a - ₀ I_ c 2 ( 3 2 a ) = ₀ a [ I_ t 2 - I_ c 3 ] ( here I_ t =J ( a² ) I_ c =J ( a² 4 ) ) = ₀ a [ a² J 2 - a² J 12 ] or, B _ R = 5 ₀ a J 12 array Comparing it with N 12 ₀ a J We get N=5

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