Physics - Magnetism Question with Solution | TestHub

Force between two parallel current carrying wires: $\mathrm{AB}$ and $\mathrm{CD}$ are two infinitely long conductors, placed parallel to each other and separated by distance $\mathrm{r}$. They carry currents ${\mathrm{I}}_1$ and ${\mathrm{I}}_2$ in the same direction.Magnetic field produced by current ${\mathrm{I}}_1$ at any point of $\mathrm{CD}$ is                 ${\mathrm{B}}_1=\frac{{\mathrm{\mu }}_0{\mathrm{I}}_1}{2\mathrm{\pi r}}$ This field acts perpendicular to $\mathrm{CD}$ and into the plane of paper. It exerts a force on wire $\mathrm{CD}$ carrying current ${\mathrm{I}}_2$. Force exerted on unit length of $\mathrm{CD}$ is                 $\mathrm{F}={\mathrm{B}}_1{\mathrm{I}}_2\mathrm{l}=\frac{{\mathrm{\mu }}_0{\mathrm{I}}_1}{2\mathrm{\pi r}}\times {\mathrm{I}}_2\times 1$                 $\mathrm{F}=\frac{{\mathrm{\mu }}_0{\mathrm{I}}_1{\mathrm{I}}_2}{2\mathrm{\pi r}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} or \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\text{·}\frac{2{\mathrm{I}}_1{\mathrm{I}}_2}{\mathrm{r}}$ By Fleming’s left hand rule, this force acts on $\mathrm{CD}$ towards $\mathrm{AB}$. Similarly, conductor $\mathrm{CD}$ also exerts an equal force $\mathrm{AB}$ towards itself. Hence the two wires get attracted towards each other, if currents are in same direction.