Three long straight conductors are arranged parallel to each other in the same plane. They carry currents of 1A , 2A and 3A in the same direction. The distance between the first two conductors is x and the distance between the second and third conductors is y . If the middle conductor is in equilibrium, then the ratio x:y is

Question

Three long straight conductors are arranged parallel to each other in the same plane. They carry currents of 1A , 2A and 3A in the same direction. The distance between the first two conductors is x and the distance between the second and third conductors is y . If the middle conductor is in equilibrium, then the ratio x:y is (A) 1:3 (B) 3:1 (C) 1:√3 (D) √3:1

Tardigrade Admin · Accepted Answer

Force per unit length between two current carrying parallel wire is given by: F=(μ 0 i1 i2/2 π r) & f12+f23=0 (μ o 1 × 2/2 π x)=(μ o 2 × 3/2 π y) (x/y)=(1/3)

$1 : 3$

$3 : 1$

$1 : 3$

$3 : 1$

Force per unit length between two current carrying parallel wire is given by :
$F = \frac{μ _{0} i _{1} i _{2}}{2 π r}$ &
$f_{12} + f_{23} = 0$
$\frac{μ _{o} 1 \times 2}{2 π x} = \frac{μ _{o} 2 \times 3}{2 π y} \frac{x}{y} = \frac{1}{3}$

1:3

3:1

1:3​

3​:1

Force per unit length between two current carrying parallel wire is given by : F=2πrμ0​i1​i2​​ & f12​+f23​=0 2πxμo​1×2​=2πyμo​2×3​yx​=31​

$1 : 3$

$3 : 1$

$1 : 3$

$3 : 1$

Force per unit length between two current carrying parallel wire is given by :
$F = \frac{μ _{0} i _{1} i _{2}}{2 π r}$ &
$f_{12} + f_{23} = 0$
$\frac{μ _{o} 1 \times 2}{2 π x} = \frac{μ _{o} 2 \times 3}{2 π y} \frac{x}{y} = \frac{1}{3}$