# Determine the points where the net magnetic field is zero

## 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:

-

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

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haruspex
Homework Helper
Gold Member
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:: -

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.

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
Homework Helper
Gold Member
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?

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
Homework Helper
Gold Member
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.

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