Three long straight. wires are connected parallel to each other across a battery of negligible internal resistance. The ratio of their resistances a.re 3:4:5. What is the ratio of distances of middle wire from the others if the net force experienced by it is zero ?

The wires are in parallel and ratio of their resistances are 3 : 4 :5- Hence currents in wires are in the ratio  $\frac{1}{3}:\frac{1}{4}:\frac{1}{5}$ Force between top and middle wire 
${\mathrm{F}}_1=\frac{{\mathrm{\mu }}_0{\mathrm{i}}_1{\mathrm{i}}_2}{2{\mathrm{\pi r}}_1}$ (r₁ = distance between these wires)
$\therefore {\mathrm{F}}_1=\frac{{\mathrm{\mu }}_0(1/3)(1/4)}{2{\mathrm{\pi r}}_1}$
Force between bottom and middle wire
${\mathrm{F}}_2=\frac{{\mathrm{\mu }}_0(1/4)(1/5)}{2{\mathrm{\pi r}}_2}$
As the forces are equal and opposite
${\mathrm{F}}_1={\mathrm{F}}_2\text{ or }\frac{1}{3{\mathrm{r}}_1}=\frac{1}{5{\mathrm{r}}_2}$
or $\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{5}{3}$