Three long parallel wires AB, CD and EF of equal resistance are connected as shown in figure. The separation between the neighbouring wires is `2*0cm` and wires AE and BF supplied to the wires and ammeter reads `12A`.
(a) or wire AB (b) of wire CD.

Answer

(a) `2*4xx10^-4Nm^-1` directed upwards (b) Zero

Explanation

As three parallel wires are of equal resistance and the total current supplied is `12A`, so current through each wire is `4A`.
(a) Force per unit length of AB due to current in CD is
`F_1=(mu_0)/(4pi)(2I_1I_2)/(r)=10^-7xx(2xx4xx4)/((2xx10^-2))`
Force per unit length of AB due to current in EF is
`F_2=(mu_0)/(4pi)(2I_1I_3)/(r_1)=10^-7xx(2xx4xx4)/((4xx10^-2))`
`=0*8xx10^-4Nm^-1`, directed upward
Total force per unit length of AB is
`F=F_1+F_2=1*6xx10^-4+0*8xx10^-4`
`=2*4xx10^-4Nm^-1` directed upwards
(b) Force per unit length of CD due to current in AB is
`F_1^'=(mu_0)/(4pi)(2I_1I_2)/(r)=10^-7xx(2xx4xx4)/((2xx10^-2))`
`=1*6xx10^-4Nm^-1` directed downwards
Force per unit length of CD due to current in EF is
`F_2^'=(mu_0)/(4pi)(2I_1I_3)/(r)=10^-7xx(2xx4xx4)/(2xx10^-2)`
`=1*6xx10^-4Nm^-1` directed upwards
`=-1*6xx10^-4Nm^-1` directed downwards
Total force per unit length of CD is
`F^'=F_1^'+F_2^'=(1*6xx10^-4)+(-1*6xx10^-4)=0`