Question

Two parallel wires P and Q placed distance r apart. They are carrying currents `I_1` and `I_2` where `I_1gtI_2`, but in opposite directions as shown in figure. Find the point on the line PQ where the resultant magnetic field is zero.

Answer 1

The resultant magnetic field will be zero at a point where the magnetic fields due to the currents in two wires are equal nad opposite. Such point R will lie to the right of Q at distance (x say) from Q.
Magnetic field at point R due to current `I_1` is
`B_1=(mu_0I_1)/(2pi(r+x))`
It is acting downwards in the plane of paper. Magnetic field at point R due to current `I_2` is
`B_2=(mu_0I)/(2pix)`
It is acting upwards in the plane of paper.
For zero magnetic field at R, `B_1=B_2`
or `(mu_0I)/(2pi(r+x))=(mu_0I_2)/(2pix)`
or `(I_1)/(r+x)=(I_2)/(x)` or `x=(I_2r)/(I_1-I_2)`