A solenoid is a common term for a wire coil used as an electromagnet. It also applies to any system that uses a solenoid to transform electric energy into mechanical energy. The system generates a magnetic field from electric current and produces linear motion using the magnetic field.
The magnetic field at the centre of the solenoid is given as:
where n is the number of turns per unit length =N/I
i is the current through the solenoid.
So, the magnetic field does not depend on the radius of the solenoid.