Two long and parallel straight wires A and B are carrying currents of 4A and 7A in the same directions are separated by a distance of 5cm. The force acting on a 8cm section of wire A is

Explanation

In between the conductors `vecB_(1)&vecB_(2)` are opposite in directions.
At the null point `B_(1)=B_(2)` which lies closer to the conductor of smaller current
`(mu_(0))/(2pi)(I_(1))/x=(mu_(0))/(2pi)(I_(2))/(r-x)rArr(I_(1))/x=(I_(2))/(r-x)`
`1/x=4/(2-x)rArr2-x=4x`
x = 0.4m from the conductor of 1A current

b) For the given situation
`B_("net")=B_(1)~B_(2)=(mu_(0))/(2pi)((I_(1))/(r//2)-(I_(2))/(r//2))=(mu_(0))/(pi)(3/2)` c) When currents are in opposite direction null point exists out side the conductors
At null point `B_(1) = B_(2)`
`(mu_(0))/(2pi)(I_(1))/x=(mu_(0))/(2pi)(I_(2))/(2+x)rArr(I_(1))/x=(I_(2))/(r+x)`
`1/x=4/(2+x)rArr2+x=4x`
`x=2/3m`