How Does an Equilateral Triangle Affect Electric Fields on Its Axis?

[various45]

Hi,

I'm trying to solve this exercize :

I/3 charges Q, positives, are at the corner of an equilateral triangle of centre O, in (x,O,y) . We want to compute the electric field created by the 3 charges on the axis z, passing by O and perpendicular at (x,O,y), thus computing the electric field E(M) in each M point of (Oz), located at an height z above O. We have OA=OB=OC.

II/ 1) Describe the symmetry plane passing by each point M, located on the axis z. Tell the sense of direction of E(M) in each point of z.

As the point M is on axis z above A, I would say (Oz) is the only symmetry plane and the electric field is from A to the low triangle.2) By a similar way, deduce the value of the electric field at the centre O

As the three charges are positives the vectorial sum of the 3 electric fields at point O would give an electric field whose value is O, but how could we deduce it by symmetry ?

3) Why would we have the electric field norm on the axis z created by the three charges reached a maximum at a unique height above O ?

I do not see how to answer this one.

Thank you very much

 

[BvU]

Hello Various (!?) , welcome to PF !

As the point M is on axis z above A, I would say (Oz) is the only symmetry plane and the electric field is from A to the low triangle.

Oz is a line, not a plane !

By a similar way, deduce the value of the electric field at the centre O

If you have brought 1) to a good conclusion, this one will be easier. There is one more symmetry plane for O

I do not see how to answer this one (3)

Again, this will be easier once we have 1) and 2).

 

[various45]

thanks for your answer,

indeed the only symmetry plane would be (ux,uz) but how could we deduve the sense according to this plane ?

 

[BvU]

Well, if, with (ux,uz) you mean the x-z plane, I don't agree !
Applying this 'symmetry' would flip the picture upside down and then it isn't the same as the original !

 

[various45]

I mean the plane which splits in two the triangle from bottom to top vertically but I do not know how to write it, until now I was doing electric field in 3D with cylindric or spheric so it was also the same planes, here we have a triangle so I would say if we take cylindric coordinate (r; theta, z) the plane (r,z) splits vertically the triangle and it is the same

 

[SammyS]

Hi,

I'm trying to solve this exercize :

I/3 charges Q, positives, are at the corner of an equilateral triangle of centre O, in (x,O,y) . We want to compute the electric field created by the 3 charges on the axis z, passing by O and perpendicular at (x,O,y), thus computing the electric field E(M) in each M point of (Oz), located at an height z above O. We have OA=OB=OC.

II/ 1) Describe the symmetry plane passing by each point M, located on the axis z. Tell the sense of direction of E(M) in each point of z.

As the point M is on axis z above A, I would say (Oz) is the only symmetry plane and the electric field is from A to the low triangle.2) By a similar way, deduce the value of the electric field at the centre O

As the three charges are positives the vectorial sum of the 3 electric fields at point O would give an electric field whose value is O, but how could we deduce it by symmetry ?

3) Why would we have the electric field norm on the axis z created by the three charges reached a maximum at a unique height above O ?

I do not see how to answer this one.

Thank you very much

Are you certain that you have a equilateral triangle?

Maybe I'm having a brain cramp, but it doesn't seem to have three sides of equal length.