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

(a) Let us call `vecB` due to (1) and (2) as `vecB_1 and vecB_2`, respectively.
At A, `vecB_1 is odot and vecB_2 is ox`
`B_1=(mu_02I)/(2pia) and B_2=(mu_0I)/(2pi2a)`
`:. B_(res)=B_1-B_2=3/4 (mu_0I)/(pia)odot`
At C, `vecB_1 is ox and vecB_2 is also ox`
`:. B_(res)=B_1-B_2=(mu_02I)/(2pia/2)+(mu_0I)/(2pia/2)=(6mu_0I)/(2pia)`
`=(3mu_0I)/(pia)ox`
At D, `vecB_1 is ox and vec B_2 is odot` and both are equal in magnitude.
`:. B_(res)=0`
(b) It is clear form the above solution that `B=0` at point 'D'.