Question

A long horizontal wire is rigidly fixed and carries 100A current. An another wire of linear mass density
2 x 10-kg/m placed below and parallel to the fixed wire. If the free wire kept 2cm below and hangs
in air, then current in free wire is :-
(1) 196 A
(2) 9 8A
(3) 4.9 A
(4) 10A​

Answer 1

Answer:

19.6 Ampere is the right answer

Answer 2

Answer:

Current in free wire is $19.6 A$

Explanation:

Let current is $w_{2}$ be $i_{2}$

Since force need to balance $m g$of $w_{2}$

So, it should be attractive or in upward direction. So current $i_{2}$ has to be parallel to $i_{1} Force per unit length =\frac{F}{L}=\frac{\mu_{0} i_{1} i_{2}}{2 \pi d}$

Mass per unit length of$\omega_{2}=\frac{M}{L}=0.2 \times 10^{-3} \mathrm{~kg} / \mathrm{m} of \omega_{2} \quad (given)$

For equilibrium of force wire

$\mathrm{F}=\mathrm{Mg}$

Or$\quad \frac{F}{L}=\frac{M}{L} g$

Or $\frac{\mu_{0} i_{1} i_{2}}{2 \pi d}=2 \times 10^{-3} \times 10$

Or $\frac{2 \times 10^{-7} \times 100 \times \mathrm{i}_{2}}{2 \times 10^{-2}}=2 \times 10^{-2}$

Or $10^{-3} \times \mathrm{i}_{2}=2 \times 10^{-2}$

Or $\mathrm{i}_{2}=2 \times 10=20 \mathrm{~A}$

$\therefore \quad i_{2}=20 \mathrm{~A}$