Two long parallel wires carrying current ` 2.5 amperes` and `I ampere` in the same direction ( directed into the plane of the paper) are held at `P and Q` respectively such that they are perpendicular to the plane of paper. The points `P and Q` are located at a distance of ` 5 metres and 2 metres` respectively from a collinear point `R` ( see figure)
(i) An electron moving with a velocity of ` 4xx10^(5) m//s ` along the positive ` x- direction ` experiences a force of magnitude `3.2xx10^(-20) N` at the point `R`. Find the value of `I`.
(ii) Find all the positions at which a third long parallel wire carrying a current of magnitude `2.5 amperes` may be placed so that the magnetic induction at `R` is zero.

Explanation

(a) Magnetic field `R` due to wires
`B = (mu_(0))/(2 pi) [(i_(1))/(5) + (i_(2))/(2)] = 2 xx 10^(-7) [(2.5)/(5) + (i)/(2)]`

Angle between `vec(v)` and `vec(B)` is `90^(@)`.
`F_(m) = B ev`
`3.2 xx 10^(-20) = 10^(-7)(1 + i)(1.6 xx 10^(-19)) (4 xx 10^(5))`
`1 + i = 5 rArr i = 4 A`
(b) Third wire can be placed left of `R` or right of `R` at distance `d`. If it is placed, left of `R` current in it should be upward ot placed right of `R`. current in it should be in downward direction.
`B_(R ) = 0`
`(mu_(0))/(2pi)[(2.5)/(5) + (4)/(2)] = (mu_(0))/(2pi)(2.5)/(d)`
`d = 1 m`