Two parallel wires p and q …

Two parallel wires P and Q placed at a separation of

6cm carry current 5A and 3A in opposite direction

respectively. Find the point on the line PQ where

resultant magnetic field is zero.

Let say at a distance of d  from Q  the magnetic field is zero

then distance from P = 6 + d

Magnetic filed ∝  Current / Distance

Mangnetic field by P   =  k  5/(6+d)  (k is Constant)

Magntic field by Q = k 3 /d  

k  5/(6+d)  =  k 3 /d

=> 5d = 18 + 3d

=> 2d = 18

=> d = 9

9 cm away from Q  & 15 cm away from P

if  current flows in same direction then Magnetic field will in between P & Q will be zero

Let say at a distance of d  from P  the magnetic field is zero

then distance from Q = 6 - d

Magnetic filed ∝  Current / Distance

Mangnetic field by P   =  k  5/d   (k is Constant)

Magntic field by Q = k 3 /(6-d)  

k  5/d  =  k 3 /(6-d)  

=> 6 (6-d) = 3d

=> 36 - 6d = 3d

=> 36 = 9d

=> d = 4

4 cm away from P towards Q