In Fig. Two long wires `W_1 and W_2`, each carrying current I, are placed parallel to each other and parallel to z-axis. The direction of current in `W_1`is outward and in `W_2` it is inward. Find `vecB` at p and Q.

Explanation

Let `vecB` due to `W_(1)` be `vecB_(1)` and due to `W_(2)` be `vecB_(2)`.
By summetry `|vecB_(1)|=|vecB_(2)|=B`
`B_(P)=2Bcos60^(@)=B=(mu_(0)I)/(2pi2a)=(mu_(0)I)/(4pia)`
`therefore vec(B_(p))=(mu_(0)I)/(4pia)hatj`

For `thetaB_(1)=(mu_(0)I)/(2pisqrt(5)a),impliesB_(2)=(mu_(0)I)/(2pia)`
`tantheta=(a)/(2a)=(1)/(2)`
`impliesvecB=(B_(1)costhetahatj)+(B_(2)-B_(1)sintheta)hati`
`sintheta=(1)/(sqrt(5))impliesvecB=(mu_(0)I)/(5pia)hatj+((mu_(0)I)/(2pia)-(mu_(0)I)/(10pia))hati`

`costheta=(2)/(sqrt(5))impliesvecB=(2mu_(0)I)/(5pia)hati+(mu_(0)I)/(5pia)hatj`