Question

Two parallel wires in free space are 10 cm apart and each carries a current of 10 A in the same direction the force exerted by one wire on the other per meter length is:

Answer 1

Hint:We will first determine the magnetic field created by the current in the first wire, and then, by making the appropriate substitutions, we will determine the force that the other wire is subjected to as a result of this magnetosphere in the nearby wire.




Formula Used:
 $F = \dfrac{{{\mu _0}{I_1}{I_2}}}{{2\pi r}}$


Complete answer:

The surrounding medium, the current flowing through it, the current of the wire on which it acts, and the distance between them all affect the force produced by the magnetic field of a current carrying wire.
The force acting due to each is acting in the same direction since the current is flowing in the same directions.
The force generated by a wire carrying current is:
$F = \dfrac{{{\mu _0}{I_1}{I_2}}}{{2\pi r}}$
Here, ${I_1}$ is the current flowing through one wire
${I_2}$is current flowing through another wire
$r$ is the separation of the two wires
The following information is provided in the question:
There are two parallel, lengthy wires that convey current.
Distance between two wires is 10cm and the current in both wires is 10A.
The force acting between the two parallel current-carrying conducting wires must be determined.$ \Rightarrow F = \dfrac{{{\mu _0}{I_1}{I_2}}}{{2\pi r}} = \dfrac{{(4\pi \times {{10}^7}) \times 10 \times 10}}{{2\pi \times 0.1}}$
$ \Rightarrow \dfrac{F}{l} = 2 \times {10^{ - 4}}N$
$\dfrac{F}{l}$ shows the force per unit length of the active conducting wire.


Note:It is important to keep in mind that the force on one wire is caused by the magnetic field of the other wire as you go through this problem. The majority of students frequently make errors when determining force on a specific wire by factoring in their own magnetic fields. The force attracts if the currents are flowing in the same direction, and repels if they are flowing in the opposite direction.