Question

Electric currents `I_1` and `I_2` are flowing in two mutually perpendicular conductors as shown in figure. Find the equation of locus of zero magnetic field points.

Answer 1

Correct Answer - an equation of a straight line
According to right hand thumb rule, the magnetic fields due to two conductors can neutralise each other only in regions I and III. Let P be a point with coordinates (x,y), where the resultant magnetic field induction perpendicular conductors is zero. Then
`B_(CD)=(mu_0)/(4pi)(2I_1)/(y)` and `B_(EF)=(mu_0)/(4pi)(2I_2)/(x)`
For zero magnetic field induction at P,
`B_(CD)=B_(EF)` or `(mu_0)/(4pi)(2I_1)/(y)=(mu_0)/(4pi)(2I_2)/(x)` or `y=I_1/I_2x`

It is an equation of a straight line.