Question

How can it be show that a magnetic field exists around a wire through which a direct electric current flowing in wire

Answer 1

If we bring a compass needle near a wire, it will show deflection which proves that there is magnetic field due to current carrying wire. The deflection is made due to the force of attraction or repulsion buy magnetic field made by the direct current (D.C) and the presence of magnet in compass.

Current carrying wire would attract another wire carrying current in the same direction and would repel if the current is in opposite direction. The direction of the magnetic field can be known by right hand thumb rule, where your thumb gives the direction of current and the curls of your finger magnetic field.