Question

The unit of electric current “ampere” is the amount of current that is flowing through each of two parallel long wires 1 m apart will give rise to a force per unit length between them equal to

• A. 1 N/m
• B. 2 × 10^-7 N/m
• C. 1 × 10^-2 N/m
• D. 4π × 10^-7 N/m

Answer 1

The correct option is B

2 × 10^-7 N/m

Step 1: Given

1. Current in Wires = I₁= I₂= 1A
2. Distance between Wires, d = 1m

Step 2: Formula Used

$F=\frac{{\mu }_o}{2\pi }\frac{L\left(I_1{I}_2\right)}{d}$

$\Rightarrow \frac{F}{L}=\frac{{\mu }_o}{2\pi }\frac{\mathit{\left(}{\mathit{I}}_{\mathit{1}}{\mathit{I}}_{\mathit{2}}\mathit{\right)}}{d}$

Where $\frac{F}{L}$ force per unit length,

${\mu }_o$ is the permeability of free space,

$I_1$ and $I_2$ are current flowing in the wires

$d$ is the distance between wires.

Step 3: Calculation

$\frac{F}{L}=\frac{{\mu }_o}{2\pi }\frac{\mathit{\left(}{I}_{\mathit{1}}{I}_{\mathit{2}}\mathit{\right)}}{d}$

$\Rightarrow \frac{F}{L}=\left[\frac{\left(4\pi \times {10}^{-7}\right)}{2\pi }\right]\left[\frac{1\times 1}{1}\right]$

$$\begin{gathered} \Rightarrow \frac{F}{L}=\left(2\times {10}^{-7}\right)\times 1 \\ \Rightarrow \frac{F}{L}=2\times {10}^{-7}N/m \end{gathered}$$

Force per unit length is 2 × 10^-7 N/m. Hence the correct option is (b)2 × 10^-7 N/m.