C12B 2011 Problem 23Finding Zero Net Magnetic Field Points in Crossed Wires

[HoneyDeeLite]

Homework Statement

Two very long fixed wires cross each other at right angles. They do not touch but are
close to each other. Equal currents flow in each wire in the directions shown below.
Indicated the locus of points where the net magnetic field is zero.


(I2)
^
|
|
|
|
------------------------> (I1)
|
|

Homework Equations

B = m0I/2pir

The Attempt at a Solution

I know from the right hand rule that the magnetic field due to I1 will curl around towards me (out of the page) on top of the wire and point away from me (into the page) when directly below the wire.
The magnetic field due to I2 will point into the page when to the right of the wire and out of the page when to the left of the wire.
But it seems that the directions of the two fields will always be perpendicular to each other and thus never cancel out. How can there be a locus of points where the net magnetic field is 0?

 

[Andrew Mason]

I am not sure why you think the fields will be mutually perpendicular since they both go into and out of the plane (ie. the plane formed by the wires).

What you want to find are points where the fields are equal in magnitude and opposite in direction.

First, in what regions will the fields be pointing in opposite directions? Then determine what condition must be satisfied for the magnitudes to be equal. Find the points in those regions where the condition is satisfied.

AM