Two long straight parallel wieres are `2m` apart, perpendicular to the plane of the paper. The wire A carries a current of `9.6 A`, directed into the plane of the paper. The wire `B` carries a current such that the magnetic field of induction at the point `P`, at a distance of `10/11` m from the wire B, is zero. find
a. the magnitude and directiion of the current in B.
b. the magnitude of the magnetic field of induction of the pont `S`.
c. the force per unit length on the wire `B`.

Explanation

(a)
Magnetic field due to wire `A` at `P`
`B_(A) = (mu_(0)(9.6))/(2pi(2 + (10)/(11)))` towards left
Since magnetic field at `P` is zero, for this magnetic field due to wire `B` should be towards right and hence current `i` in wire `B` should be in upward direction.
`B_(B) = (mu_(0)i)/(2pi (10//11))` towards right
`B_(a) = B_(B)`
`(mu_(0)(9.6))/(2 pi(2 + (10)/(11))) = (mu_(0)i)/(2pi((10)/(11)))`
`9.6 xx (10)/(11) = i xx (2 + (10)/(11) = (32)/(11))`
(b)
`(1.6)^(2) + (1.2)^(2) = 2^(2) = 2^(2) i.e lt ASB = 9-0^(@)`
`B_(A) = (mu_(0)(9.6))/(2pi(1.6)) = (3mu_(0))/(pi)`, along `SB`
`B_(B) = (mu_(0)(3))/(2pi(1.2)) = (5 mu_(0))/(4pi)`, along `SA`
`B_(S) = sqrt(B_(A)^(2) + B_(B)^(2)) = (mu_(0))/(pi)sqrt((3)^(2) + ((5)/(4))^(2))`
`= (mu_(0))/(4pi) xx 13 = 13 xx 10^(-7)T`
( c) Force per unit length on the wire `B`
`F = (mu_(0) i_(A)i_(B))/(2pi d) = (2 xx 10^(-7) xx 9.6 xx 3)/(2)`
`= 28.8 xx 10^(-7) N//m`, repulsion