Why is itthat if a current carrying loop has n turns the field produced atany point is n times as large as that produced by a single turn

The magnetic field produced by a current-carrying loop is directly proportional to the number of turns in the loop. This is due to the principle of superposition, which states that the total magnetic field at a point is the vector sum of the individual magnetic fields at that point.

Here are the steps to understand this:

1. Consider a single loop of wire carrying a current. According to Ampere's Law, this loop will produce a magnetic field around it. The strength of this field is directly proportional to the current flowing through the loop.

2. Now, if we add another identical loop (with the same current) to the first one, the total magnetic field at any point will be the sum of the magnetic fields produced by each loop. This is because the magnetic field is a vector quantity, and vectors add up.

3. Therefore, if we have n identical loops (each carrying the same current), the total magnetic field at any point will be n times the magnetic field produced by a single loop. This is why the magnetic field produced by a current-carrying loop is n times as large as that produced by a single turn.

4. This principle applies as long as the loops are close enough together that the magnetic field of each loop overlaps significantly with the others. If the loops are too far apart, the magnetic fields may not add up in this way.