Question

$\text{A, B}$ and $\text{C}$ are parallel conductors of equal length carries currents $I,I$ and $2I$ respectively. Distance between $\text{A}$ and $\text{B}$ is $x$. Distance between $\text{B}$ and $\text{C}$ is also $x$. $F_1$ is the force exerted by $\text{B}$ on $\text{A}$ and $F_2$ is the force exerted by $\text{C}$ on $\text{A}$. Find the correct relation-

• A. $F_1=2F_2$
• B. $F_2=2F_1$
• C. $F_1=F_2$
• D. $F_1=-F_2$

Answer 1

The correct option is C $F_1=F_2$

Force per unit length between two parallel current carrying conductors is,

$F=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}....\left(1\right)$

Using (1) we get,

$F_1=\frac{{\mu }_0{I}^2}{2\pi x}$

$F_2=\frac{2{\mu }_0{I}^2}{2\pi \left(2x\right)}=\frac{{\mu }_0{I}^2}{2\pi x}$

$\therefore F_1=F_2\left[\text{In the same direction}\right]$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.