Question

Current of 10 ampere and 2 ampere are passed through two parallel wires A and B, respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2 m, the force on the conductor B which is situated at 10 cm distance from A will be

• A. $8\times {10}^{-5}N$
• B. $4\times {10}^{-5}N$
• C. $8\pi \times {10}^{-7}N$
• D. $4\pi \times {10}^{-7}N$

Answer 1

The correct option is A $8\times {10}^{-5}N$

Using Amper's law $\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_0{i}_{enclosed}$
$\therefore B=\frac{{\mu }_0{i}_{enclosed}}{2\pi r}=\frac{4\pi \times {10}^{-7}\times 10}{2\pi \times (10\times {10}^{-2})}=2\times {10}^{-5}T$
Force on the conductor $B$ is $F=ilB=2\times 2\times (2\times {10}^{-5})=8\times {10}^{-5}N$