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Question

In two current carrying conductors parallel currents ________ , anti parallel currents _________


A

attract

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B

repel

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Solution

Step 1: Two Current Carrying Conductors

Let us consider two long parallel wires, (1 and 2) carrying currents I1 and I2, separated by a distance a. The conductor 1 produces a magnetic field

B1=μ04π.2I1a

At the position of conductor 2. It is directed perpendicular to the conductor 2.

The force dF acting on the element dl2 of the conductor 2 due to B1 is

dF=I2dl2×B1

dF=dF=μ04π.2I1I2adl2

Step 2: Nature of attraction

This force is directed towards the conductor 1, i.e., attractive if I1 and I2 flow in the same direction.

On the other hand, the force is directed away from the conductor 1 if I1 and I2 flow in opposite directions.

The type of force is dependent on the magnetic flux around the two conductors.

The force per unit length of each wire is of magnitude

F=μ04π.2I1I2a

And directed perpendicular to their lengths.

Hence, in two current-carrying conductors parallel currents attract, and anti-parallel currents repel.


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