Question

The force between two parallel conductors, each of length $50\text{m}$ and distance $20\text{cm}$ apart, is ${10}^{-2}\text{N}$. If the current in one conductor is double to that in another one, then their values will respectively be

• A. $10\text{A}$ and $20\text{A}$
• B. $50\text{A}$ and $100\text{A}$
• C. $5\text{A}$ and $10\text{A}$
• D. $25\text{A}$ and $50\text{A}$

Answer 1

The correct option is A $10\text{A}$ and $20\text{A}$

Magnetic force between two parallel conductors is given by,
$$F_B=\frac{{\mu }_0{i}_1{i}_{2}L}{2\pi d}$$Given,

The length of the conductors, $L=50\text{m}$

Distance between the conductors, $d=20\text{cm}$

$F_B={10}^{-2}\text{N}$

and $i_1=2i_2$

$\therefore {10}^{-2}=\frac{2\times {10}^{-7}\times 2i_2^2\times 50}{0.2}$

$\Rightarrow i_2=10\text{A}$

$\therefore i_1=20A$

Hence, option (a) is the correct answer.