I have read that a current carrying conductor produces a magnetic field around it. Does this apply to the power supply lines also? Can they deflect a compass needle when kept under it?
Anything that carries current generates a magnetic field. The magnitude and direction of this field is determined by the magnitude and direction of the current. So, for a constant DC current, the magnetic field is also constant, and a compass needle deflects to align with it.
Power lines, however, do not carry constant DC current. They carry AC current with a frequency of 60 Hz. Therefore, the direction of the magnetic field changes 60 times per second, which means it causes no visible deflection of the needle. However, if you were to take a very high-framerate and magnified video of the compass needle and slow it down, you would see a small vibration in the needle caused by the field.