Two parallel wires P and Q placed at a separation
` d= 6 cm` carry electric currents `i_1= 5A` and `i_2= 2A` in `
` opposite directions as shown in figure. Find the`
` point on the line PQ where the resultant magnetic field `
is zero.

Explanation

Solution: At the desired point, the magnetic fields due to
the two wires must have equal magnitude but opposite
directions. The point should be either to the left of P or
to the right of Q. As the wire Q has smaller current, the
point should be closer to Q. Let this point R be at a
distance x form Q( figure 35-W2b).
The magnetic field at R due to the current `i_1` will have
magnitude
` B_1 = (((mu_0)(i_1))/2 pi ( d + x))`
and will be directed downward in the plane of the figure.
The field at the same point due to the current `i_2` will be
` B_2= ((mu_0)(i_2)/2 pi x)`
` directed upward in the plane of the figure. If the`
` resultant field at R is zero, we should have B_1 =B_2 , so `
that
` ((i_1 )/(d+x))= i_2/ x`
` giving, x = ((i_2)d/(i_1- i_2) `
` = ((2A)(6cm)/(3A)) = 4 cm.`