A steady current I flows along an infinitely long hollow cylindrical conductor of radius R . This cylinder…

A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed co-axially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is(are):
  1. In the region 0<r<R, the magnetic field is non-zero.
  2. In the region R<r<2R, the magnetic field is along the common axis.
  3. In the region R<r<2R, the magnetic field is tangential to the circle of radius r, centered on the axis.
  4. In the region r>2R, the magnetic field is non-zero.

Solution

If we consider a point at a distance r from a common axis such that 0<r<R, the magnetic field is non-zero because inside infinite solenoid magnetic field is, B→ = μ0ni and due to the hollow cylinder it is zero.  Hence, net magnetic field is non-zero. 

If 2R<r, then magnetic field due to an infinite solenoid is zero but there will be a non-zero magnetic field because of hollow cylinder. Hence, net magnetic field is non-zero.

If R<r<2R, then the magnetic field due to solenoid is along the axis and magnetic field due to the hollow cylinder is in circular form. Hence, the net magnetic field is neither along axis nor in tangential direction.

Asked in: JEE Advanced 2013 (Paper 2)

Practice more Magnetic Fields due to Electric Current questions on Aicharya