JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Magnetic Effects of Current

**For $0<r<R$:** Inside the hollow cylinder, the magnetic field due to the cylinder is zero (by Ampere's law, no current enclosed). However, the point is inside the solenoid, so $B={\mu }_{0}nI\ne 0$. ✓ (A)

**For $R<r<2R$:** The cylinder produces a tangential field $B=\frac{{\mu }_{0}I}{2\pi r}$, and the solenoid produces an axial field $B={\mu }_{0}nI$. The net field is neither purely axial nor purely tangential. ✗ (B, C)

**For $r>2R$:** Outside the solenoid, its field is zero. But the cylindrical conductor still produces a tangential field $B=\frac{{\mu }_{0}I}{2\pi r}\ne 0$. ✓ (D)