Two long parallel consuctors `S_(1) and S_(2)` are separated by a distance 10 cm and carrying of 4A and 2A respectively . The conductors are placed along x axis in X-Y plane . There is a point P located between the conductors (as shown in figure ).
A charge particle of `3pi` coulomb is passing through the point P with velocity `vec(v) = (2hat(i)+3hat(j))`m/s , where `hat(i) & hat(j)` represents unit vector along x & y axis respectively .
The force acting on the charge particle is `4pi xx 10^(-5) (-xhat(i) +2hat(j))N` . The values of x is :

Options

A. 2
B. 1
C. 3
D. `-3`

Answer

C

Explanation

`B_(Net) = (mu_(0)4)/(2pi xx4/100)-(mu_(0)2)/(2pixx6/100)`
`= (mu_(0))/pi xx 100[1/2 -1/6]`
` = (mu_(0))/pi xx 100[4/(2xx6)]`
`=(mu_(0)xx100)/(3pi) (-hat(k))`
`vec(F) = 9(vec(V)xxvec(B)) = 3pi [2hat(i) +3hat(j)] (mu_(0)xx100)/(3pi) (-hat(k))`
`= 4pi xx 10^(-7) [2hat(i) +3hat(j)]xx 100(-hat(k))`
` = 4pi xx 10^(-5) [2hat(j)-3hat(i)]`
` :. x = 3 `