Question

Consider three long straight parallel wires as shown in figure. Find the force experienced by $25\text{cm}$ length of wire $C$.

• A. $3\times {10}^{-4}\text{N}$ towards right
• B. $3\times {10}^{-4}\text{N}$ towards left
• C. Zero
• D. $4\times {10}^{-4}\text{N}$ towards right

Answer 1

The correct option is B $3\times {10}^{-4}\text{N}$ towards left

Force on wire $C$ due to wire $\text{D}$ will be directed towards left and its magnitude will be,

$F_1=\frac{{\mu }_0{i}_1{i}_{2}L}{2\pi r}$

$=\frac{(2\times {10}^{-7})(30\times 10)}{3\times {10}^{-2}}\left(0.25\right)$

$=5\times {10}^{-4}\text{N}$

Similarly, force on wire $C$ due to wire $\text{G}$ will be directed towards right and its magnitude will be,

$F_2=\frac{(2\times {10}^{-7})(20\times 10)}{5\times {10}^{-2}}\left(0.25\right)$


$=2\times {10}^{-4}\text{N}$

$\therefore F_{net}=F_1-F_2$$=3\times {10}^{-4}\text{N}$

Its direction will be towards left as
$|{\overrightarrow{F}}_1|>|{\overrightarrow{F}}_2|$

Therefore, option $\left(B\right)$ is correct.