Determine the points where the net magnetic field is zero

[jisbon]

Homework Statement

A long straight wire lying along x axis carries current I in positive x direction.
Another long straight wire lying along y axis carries current I/3 in positive y direction.
Find points where net magnetic field is zero.

Relevant Equations

-

Unsure about this, but here is my attempt:

B from the first wire: $\dfrac {\mu _{0}I}{2\pi r}$

B from the second wire: $\dfrac {\mu _{0}I}{2\pi r}$

Let the point be (x,y)

Can I state that: $\dfrac {\mu _{0}I}{2\pi y}+\dfrac {\mu _{i}\left( I/3\right) }{2\pi x}=0$

Hence the magnetic field is zero whenever x= -1/3y?

Thanks

 

[haruspex]

Homework Statement:: A long straight wire lying along x-axis carries current I in positive x direction.
Another long straight wire lying along y-axis carries current I/3 in positive y direction.
Find points where net magnetic field is zero.
Relevant Equations:: -

Unsure about this, but here is my attempt:

B from the first wire: $\dfrac {\mu _{0}I}{2\pi r}$

B from the second wire: $\dfrac {\mu _{0}I}{2\pi r}$

Let the point be (x,y)

Can I state that: $\dfrac {\mu _{0}I}{2\pi y}+\dfrac {\mu _{i}\left( I/3\right) }{2\pi x}=0$

Hence the magnetic field is zero whenever x= -1/3y?

Thanks

The magnetic field is a vector. You need the vector sum to be zero.

 

[jisbon]

The magnetic field is a vector. You need the vector sum to be zero.

So for example in the wire on y axis, can't I assume it will only affect the x direction as the y direction is simply canceled out?

 

[haruspex]

So for example in the wire on y axis, can't I assume it will only affect the x direction as the y direction is simply canceled out?

Certainly the field due to that wire nowhere has a y component. What does that leave?

 

[jisbon]

Certainly the field due to that wire nowhere has a y component. What does that leave?

So that leaves a x component, while the wire at the x-axis only leaves the y component, hence the equation I put in my thread whereby:
$\dfrac {\mu _{0}I}{2\pi y}+\dfrac {\mu _{i}\left( I/3\right) }{2\pi x}=0$

 

[haruspex]

So that leaves a x component

I do not read the question as restricted to a plane.
Besides, an x component cannot cancel a y component.

 

[jisbon]

I do not read the question as restricted to a plane.
Besides, an x component cannot cancel a y component.

So the x component must be equals to 0 too? since the point I am trying to find has no magnetic field

 

[haruspex]

So the x component must be equals to 0 too? since the point I am trying to find has no magnetic field

Yes, but but what about my other point? The Newtonian world has three dimensions.