Question

The force between two parallel conductors, each of length $50m$ and distant $20cm$ apart, is $1N$. If the current in one conductor is double than that in another one, then their values will respectively be :

• A. $100A$ and $200A$
• B. $50A$ and $400A$
• C. $10A$ and $30A$
• D. $5A$ and $25A$

Answer 1

Answer: (A)

$100A$ and $200A$

Given that,
$F=1N$,$l=50m$,$r=20cm=0.2m$,$i_2=2i_1$

The force between two long parallel conductors separated by distance r, is
$F=\frac{{\mu }_0\left(i_1\right)\left(i_2\right)l}{2\pi r}$
$F=\frac{(4\pi \times {10}^{-7})\left(i_1\right)\left(2i_1\right)50}{2\pi 0.2}$
$i_1^2=\frac{2\pi \left(0.2\right)}{(8\pi \times {10}^{-7})50}$
$i_1^2=\frac{0.2}{(200\times {10}^{-7})}$
$i_1^2=10000$
$i_1=100A$
and $i_2=2i_1=200A$