Question

Using diagrams and explanations of the two right-hand rules required, explain why there is an attractive force between two parallel currents.

Answer 1

Right hand rule-1 : If your index finger of the right hand is directed towards the current and the middle finger is directed towards the magnetic field, then you thumb will point the magnetic force on the conductor.

Right hand rule-2 : If we grasp the straight conductor in our right hand thumb points in the direction of the current then the fingers curl in the direction of the magnetic field B with the fingertips pointing along magnetic field.

Suppose two wires PQ and RS are two parallel wires placed in the plane of paper, and carry currents i_{​​​​​​1} and i_{​​​​​​2} in the same direction.

The magnetic field B_{​​​​​​1}​​​​​ at any point on RS due to the current i_{​​​​​​1} in PQ is directed into the page according to the right hand rule-2. The the conductor RS, carrying current I_{​​​​​​2}, is thus situated perpendicular to the magnetic field B_{​​​​​​1} . It therefore experiences a magnetic force towards the conductor PQ according to the right hand rule- 1.

The magnetic field B_{​​​​​​2} at at any point on PQ due to the current i_{​​​​​​2} in RS is directed out of the page according to the right hand rule-2. The conductor PQ carrying current i_{​​​​​​1}​​​​​ , is does situated perpendicular to the magnetic field B_{​​​​​​2} . It therefore experiences a magnetic force towards the conductor RS according to the right hand rule-2.

So the forces on the conductors are directed towards each other i.e. there is an attractive force between two parallel wires if they carry currents in the same direction.