Question

The unit of electric current is ‘ampere’ which is the current, when flowing through each of two parallel wires spaced 1 m distance apart in vacuum and these two wire is of infinite length will give rise to a force between them equal to which of the following
(A) \[1\,N/m\]$$
(B) $2 \times {10^{ - 7\,}}N/m$
(C) $1 \times {10^{ - 2}}\,N/m$
(D) $4\pi \times {10^{ - 2\,}}\,N/m$

Answer 1

Hint: Start with finding the relation between the force between the two parallel wires, current flowing through each wire, length of the wire and the distance between the two parallel wire. Then put all the values provided in the question in the required relation and finally you will get the force between the two wires.

Complete answer:
First start with the given information in the question:
Distance between the two parallel current carrying wire is 1 m.
Current flowing through the first wire, ${i_1} = 1\,A$
Current flowing through the second wire, ${i_2} = 1\,A$

Now we know that, force between the two current carrying parallel wire will be;
$F = \left( {\dfrac{{{\mu _0}}}{{2\pi }}} \right)\left[ {\dfrac{{\left( {{i_1}{i_2}l} \right)}}{y}} \right]$
Where, y is the distance between the two wire.

Substituting all the values in the equation of force, we get;
$\dfrac{F}{l} = \left[ {\dfrac{{\left( {4\pi \times {{10}^{ - 7}}} \right)}}{{2\pi }}} \right] \times \left[ {\dfrac{{\left( {1 \times 1} \right)}}{1}} \right]$
$\dfrac{F}{l} = 2 \times {10^{ - 7}}\,N/m$

Therefore, the force between the two parallel current carrying wire will be $2 \times {10^{ - 7}}\,N/m$

Hence the correct answer is Option(B).

Note: Here the two wire was parallel to each other if it not then the formula for the force between the two current carrying wire will get changed. Also the distance, current between them was same but it is not the case all the time so be careful before putting these value in the equation of force between the two wire.