The correct instrument to determine the presence of a magnetic field is option 3, the magnetic needle. A magnetic needle is a simple compass needle, often made of a magnetized material such as iron or steel, that aligns itself with the magnetic field in which it is placed. When exposed to a magnetic field, the needle will align itself with the direction of the field lines, showing the presence of the field.

Option 1, the ammeter, is used to measure electric current in a circuit and is not directly related to detecting magnetic fields.

Option 2, the voltmeter, is used to measure the voltage difference between two points in an electrical circuit and is not directly used for detecting magnetic fields.

Option 4, the motor, is a device that converts electrical energy into mechanical energy. While motors often utilize magnetic fields, they are not specifically designed to detect the presence of a magnetic field.

In conclusion, the correct instrument for determining the presence of a magnetic field is the magnetic needle.