A tightly- wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surgace current through a width dl of the sheet is Kdl and the number of turns per unit length of the solenoid is n. The magnetic field near the centre of the solenoid is found to be zero. (a) find the current in the solenoid. (b) If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its centre?

Explanation

To solve the given problem, we will break it down into two parts as specified in the question.

### Part (a): Finding the Current in the Solenoid

1. **Understanding the Setup**:
- We have a long solenoid with a number of turns per unit length \( n \).
- There is a large metal sheet carrying a surface current \( K \) through a width \( dl \).
- The magnetic field at the center of the solenoid is zero.
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