In Fig. There are two parallel long wires (placed in the plane of paper ) carrying currents 2I and I. Consider point A,C and D on the line perpendicular to both the wires and also in the plane of the paper. The distances are mentioned. Find (a) `vecB` at A,C and D (b) position of points on line ACD where `vecB` 0 is.

Explanation

(i) Let us call `vecB` due to (1) and (2) as `vecB_(1)andvecB_(2)` respectively . Then at `A:vecB_(1)` is `odotandvecB_(2)` is `otimesB_(1)=(mu_(0)2I)/(2pia)andB_(2)=(mu_(0)I)/(2pi2a)`
`thereforeB_("res")=B_(1)-B_(2)=(3)/(4)(mu_(0)I)/(pia)odot`
at `C:vecB_(1) " is "otimesandvecB_(2) " also "otimes`
`thereforeB_("res")=B_(1)+B_(2)=(mu_(0)2I)/(2pi(a)/(2))+(mu_(0)I)/(2pi(a)/(2))`
`=(6mu_(0)I)/(2pia)=(3mu_(0)I)/(pia)otimes`
at `D:vecB_(1) " is "otimes andvecB_(2) "is " odot` and both are equal in magnitude.
`thereforeB_("res")=0`
(ii) It is clear from the above solution that B=0 at point 'D'.