A tightly-wound, long solenoid is initially kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through a width dl of the sheet is K , dl and the number of turns per unit length of the solenoid is n . In this initial orientation, the magnetic field near the centre of the solenoid is found to be zero. If the solenoid is subsequently rotated to make its axis perpendicular

Step-by-step solution

The magnetic field produced by a large metal sheet carrying a surface current density K is uniform and parallel to the sheet. By Ampere's law, its magnitude is given by: B_ sheet = ₀ K 2 Initially, the solenoid's axis is parallel to the sheet, and the net magnetic field at its centre is zero. This implies that the magnetic field produced by the solenoid exactly cancels the magnetic field of the sheet. Therefore, the magnetic field of the solenoid must be equal in magnitude and opposite in direction to the field of