Question

In the SI system, the unit of current, the ampere, is defined by this relationship using an apparatus called an Ampere balance. What would be the force per unit length of two infinitely long wires, separated by a distance 1 m, if 1 A of current were flowing through each of them? Express your answer numerically in newtons per meter. F/L = N/m

Answer 1

Answer:

$\dfrac{F}{l}=2\times 10^{-7}\ N/m$

Explanation:

It is given that,

Distance between two infinitely long wires, d = 1 m

Current flowing in both of the wires, I = 1 A

The magnetic field in a wire is given by :

$B=\dfrac{\mu_oI}{2\pi d}$

The force per unit length acting on the two infinitely long wires is given by :

$\dfrac{F}{l}=\dfrac{\mu_o I_1I_2}{2\pi d}$

$\dfrac{F}{l}=\dfrac{4\pi \times 10^{-7}\times 1^2}{2\pi \times 1}$

$\dfrac{F}{l}=2\times 10^{-7}\ N/m$

So, the force acting on the parallel wires is $2\times 10^{-7}\ N/m$. Hence, this is the required solution.