The magnetic field lines around the current-carrying straight wire is shown as below:

The direction of magnetic field lines can be determined using Right-Hand Thumb Rule.

Solenoid is a type of electromagnet formed by wrapping a insulated wire coil around a soft iron.

A picture showing the magnetic field developed around a solenoid:

If direction of current in a solenoid is known, the magnetic field developed around it can be determined by the use of Maxwell's right hand thumb rule as well.