Question

Two very long wire parallel to each other and separated by a distance 1m apart. If current in both the wires is 1A, then the force per unit length on both wire will be :
a) $2 \times {10^{ - 7}}$
b) ${10^{ - 7}}$
c) $3 \times {10^{ - 7}}$
d) $4 \times {10^{ - 7}}$

Answer 1

Hint: In order to solve this question, we will use the general relation between the force acting between two parallel current carrying conductors when placed nearby to each other and using given conditions and parameters value we will solve for force per unit length of the wire.

Complete answer:
Look there is two current carrying conductor. A current flowing through a metal wire creates a magnetic field. This magnetic field can be used to produce electric current in another wire. The strength of the magnetic field created by a current depends on the amount of current flowing through the wire and the distance between the wires.

When two parallel wires are carrying currents in the same direction, the currents attract each other and if current flows in opposite direction then they are repel each other. Now we are clear about the concept then lets make a picture of the question.

First find the magnetic field. We know the formula
$\vec B = \dfrac{{\mu _0^{}I}}{{2\pi r}}\hat z$
here,
$B = {\text{ magnetic field, }}{\mu _0} = {\text{ parmeability, }}$
$r = {\text{distance form the wire, }}$
$I = {\text{ current}, {\hat z}} = {\text{a unit vector towards into plane}}$ .

Or,
$\dfrac{{4\pi \times {{10}^{ - 7}} \times 1}}{{2\pi \times 1}} = 2 \times {10^{ - 7}}$ Tesla.

So we get the magnetic field. Now find out the force due to this magnetic on the second wire. Here the formula is
$F = ilB$ where $i = {\text{current, l = length of the wire ,B = magnetic field}}$ .
or,
$F = 1 \times 1 \times 2 \times {10^{ - 7}}N = 2 \times {10^{ - 7}}N$ .

So our final answer is $2 \times {10^{ - 7}}N$ . Hence option a is the correct.

Note: While solving such questions, firstly don’t forget to convert all the required physical quantities in same standard units and additionally, we should know that when the current in both wires is in same direction then there is force of attraction and when current is opposite direction wires repel each other.