Question

Two long parallel wires separated by a distance $R$ have equal current $I$ flowing in each. The magnetic field of one exerts a force $F$ on the other.The distance $R$ is increased to $2R$ and the current in each wire is reduced from $I$ to $0.5I$. Now the force between them is

• A. $4F$
• B. $F$
• C. $0.25F$
• D. $0.125F$

Answer 1

Answer: (D)

$0.125F$

Force between them $F=\frac{{\mu }_0{i}_1{i}_2.\partial l}{2\pi r}$
$F=\frac{{\mu }_0{I}^2.\partial l}{2\pi r}$
And $F^{\prime }=\frac{{\mu }_0\left(\right(\frac{I}{2}{)}^2).\partial l}{2\pi \times 2r}$
$F^{\prime }=\frac{F}{8}$