Question

Two parallel wires carry electric current in same direction. The wires

• A. attract each other
• B. repel each other
• C. do not attract or repel
• D. oscillate

Answer 1

The Correct Option is B

repel each other

Answer 2

Let us consider two infinitely long straight wires. Let the two wires be placed free and along with that parallel to each. The two wires carry currents i1 and i2. However, the directions of the both currents are to the opposite of each other. Let the perpendicular distance between them be d.

 

 By observing the above figure, the direction of current in the left wire is inside the plane of the page and that of the current in the other wire is outside the same plane.

So, if we analyse the influence of wire 1 on the wire 2.

An infinitely long straight wire, which is carrying some current, produces the magnetic field lines in the surroundings in the form of the concentric circles. So, the centre of these circles is on the axis of wire 1 and the direction of the magnetic field is given by the right hand rule.

Therefore, according to the right hand rule, the direction of the magnetic field lines due to current in wire 1 is in the clockwise direction.

 So, when a straight current carrying conductor is placed in the external magnetic field, the conductor experiences the magnetic force given as \(\underset{F}{\rightarrow}=i(\underset{L}{\rightarrow}\times\underset{B}{\rightarrow})\)

As here, i is the current in the conductor, \(\underset{L}{\rightarrow}\) is the length vector of the conductor and the direction of it is along the direction of the current in the conductor. \(\underset{B}{\rightarrow}\) is the external magnetic field at the point where we are finding the force.

Hence, the direction of the magnetic force is perpendicular to the plane in which 

\(\underset{L}{\rightarrow}\) and \(\underset{B}{\rightarrow}\) lie.

 So, now we can understand that wire 1 will create an external magnetic field for wire 2. Hence, as the result wire 2 experiences a magnetic force.

So, now let us calculate the direction of the magnetic force.

The direction of the magnetic field at the location of wire 2 will be in the downwards direction. Let us assume the magnetic field is \(\underset{B}{\rightarrow}_{2}\). For wire 2, \(\underset{L}{\rightarrow}\) is directed outside the plane as the current is coming from outside of the plane.

Hence, the direction of the magnetic force on wire 2 is in the direction of the vector of 

(\(\underset{L}{\rightarrow}\)×\(\underset{B}{\rightarrow}\)). Which comes out to be directed towards the right.

So, this means that wire 1 applies a force on the wire 2 such that it pushes it away from itself.

Now for the influence of wire 2 on the wire 1 repeat the analysis from the other side of the plane and you can find a similar influence of wire 2 on wire 1.

Hence, wire 2 will also apply a force on wire 1 that pushes it away from itself.

 So, the correct answer is “Option B”.