Question

Two parallel wires of length 9m each are separated by a distance 0.15m. If they carry equal currents in the same direction and exert a total force of $30\times {{10}^{-7}}$N on each other than the value of current must be
A. 2.5A
B. 3.5A
C. 1.5A
D. 0.5A

Answer 1

Hint: In the question it is given that both the wires are carrying current in the same direction. It implies that the force acting will be an attractive force. So to solve this question we will use the formula of force per unit length.

Formula used:
Force experienced,
$F=\dfrac{{{\mu }_{0}}{{I}_{1}}{{I}_{2}}l}{2\pi d}$
Where,
$µ_0$ is the permeability of free space
$I_1$ is the current flowing through one conductor
$I_2$ is the current flowing through second conductor
l is the length of the conductor
d is the distance between the two conductors

Complete answer:
The current carrying conductor experiences a magnetic field and due to which they experience a force. This force is attractive when the direction of current carried by both the conductors is the same.
This force becomes repulsive when current flowing through any of the conductors is reversed.
We use the above equation to find the current flowing through both the conductors. Here the current flowing through both the conductors is the same.

Therefore, equation for force experienced by both the conductor becomes:
$F=\dfrac{{{\mu }_{0}}{{I}^{2}}l}{2\pi d}$

In this question it is given that,
Force experienced by both the conductor, F=$30\times {{10}^{-7}}$N
Length of two parallel wires, l= 9m
Distance between conductor, d= 0.15m

On substituting values, we get current flowing through the conductor as:
$I=\sqrt{\dfrac{30\times {{10}^{-7}}\times 2\pi \times 0.15}{4\pi \times {{10}^{-7}}\times 9}}$
Therefore, current flowing is $I=0.5A$

Therefore, the answer is option (D).

Note: The problem can be solved by using $F=i\left(\vec {l} \times \vec {B}\right)$ or $F=iBl$ also. Here we need to find the value of magnetic field B and substitute in the equation. While solving this way we have to be carefully analyse the direction of B. The problem solving becomes easy as the currents are flowing in the same direction. Any of the methods can be followed to arrive at the solution.