Electric Field Direction at Point z=a for Two Perpendicular Lines of Charge

[Bradracer18]

I've got one more question for you guys. I am having a hard time understanding the problem, and thus can't solve it.

A long line of charge with charge per unit length lamda1 is located on the x-axis and another long line of charge with charge per unit length lamda2 is located on the y-axis with their centers crossing at the origin. In what direction is the electric field at point z=a on the positive z-axis if lamda1 and lamda2 are positive?

A. the positive z direction
B. the negative z direction
C. halfway between the x direction and the y direction
D. all directions are possible parallel to the xy plane

Any help understanding this problem would be great...and I'm sure I'll need some guidance in solving it. I really don't understand the "point z=a" portion of the question. Do I use the right hand rule here??

Thanks guys!
Brad

 

[Astronuc]

For positive charges, the E (vector) field points away from the charge.

Use the right hand rule for orientation of + axis, and think of the x,y plane.

Is the charge along the x and y-axis symmetrical, i.e. extending to -infinity,+infinity, or at least from -a to +a, where a is some distance. In that case the E-components perpendicular to z-axis cancel for the same charge located symmetrically.

See - http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/efiecon.html

and (perhaps later)

http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/elecyl.html#c1

 

[arunbg]

I think it can be either A or B if it is indeed the scenario explained by Astronuc depending on the sign of lamda .

 

[Bradracer18]

Well I'm not sure if I'm right or not...but yeah I had the same argument as arunbg had. I used my right hand rule...and came up with it pointing towards the positive z direction(using lamda as +)...and I guess if you use lamda as - then it would be in the negative z direction. I assume since they didn't say negative lamda...then we can assume it is positive? So...as of right now I'd go with answer A...is this correct...or am I misleading myself once again...??

Thanks all!
Brad


****Edit...just re-read the question...and the last line says find direction of electric field at z=a on positive z-axis...if both lamda's are positive...

 

[nrqed]

Well I'm not sure if I'm right or not...but yeah I had the same argument as arunbg had. I used my right hand rule...and came up with it pointing towards the positive z direction(using lamda as +)...and I guess if you use lamda as - then it would be in the negative z direction. I assume since they didn't say negative lamda...then we can assume it is positive? So...as of right now I'd go with answer A...is this correct...or am I misleading myself once again...??

Thanks all!
Brad


****Edit...just re-read the question...and the last line says find direction of electric field at z=a on positive z-axis...if both lamda's are positive...

There is no right hand rule involved in this problem! If you are using a right hand rule it's probably because you are thinking of a magnetic field produced by a current. That's not at all the situation here.

The E field of an infinite line of charge points radially away from the line if the charge is positive. If there are two lines of charge, one must do a vector sum of the two E fields and the result depends on where the point is and its distance from the two lines. In this particular example, you have a lucky break since at the point indicated, the E fields of the two lines of charge are pointing in the same direction so that it's obvious what the direction of the vector sum of the two is. Do you see this?

Patrick

 

[Bradracer18]

I understand what you are saying now...not sure I know how to do the vector sums though...Is it C??

 

[nrqed]

I understand what you are saying now...not sure I know how to do the vector sums though...Is it C??

I think you should first make sure that you visualize the situation.

First, let's say there is only one line of charge, ok? It's located along the x axis. Can you visualize the point at z=+a? (if the xy plane is in the plane of a sheet of paper, the point z=a is *above* the sheet of paper, right?). What would be the direction of the E field at the point z=a?

You must think in 3 dimensions for this problem.

Now consider if there is only a line along the y axis.

Finally put the two lines together and visualize doing a vector sum of the two E fields.

Patrick

 

[Bradracer18]

Ok...yes I can visualize that. I can think in 3D(used to draw on autocad). So...both points would be in the positive z direction then, right?
Or that is how I see it anyways. I'm not sure though, what answer D means, so that may be an option too...

 

[nrqed]

Ok...yes I can visualize that. I can think in 3D(used to draw on autocad). So...both points would be in the positive z direction then, right?
Or that is how I see it anyways. I'm not sure though, what answer D means, so that may be an option too...

Ok. But first thing first. If there was only one line of charge (say the one along the x axis), what would be the direction of the E field at th epoint?

 

[Bradracer18]

Well...I thought above we decided it would be out from the x plane...towards the positive z plane(I guess is what I'd call it)...or as you said before too...it would point radially away from the charge...

 

[nrqed]

Well...I thought above we decided it would be out from the x plane...towards the positive z plane(I guess is what I'd call it)...or as you said before too...it would point radially away from the charge...

You have to be careful about the wording. The expression "x plane" does not quite make sense. There is the xy plane, the xz plane and the yz plane. I think you mean "away from the xy plane" here. I am not sure what you mean by "toward the positive z plane" either!
I think you mean "in the positive z direction", right? (which means in the direction that the z axis is pointing".

I am not being difficult here. It's just that without the right expression, it is impossible to communicate effectively.

Now what if there is only a line of charge along the y axis. What can you say about the direction of the electric field vector at the point z=a?

Now what if both lines of charge are there?
(imagine doing a vector sum of th etwo E fields you found previously)

That should give you the answer.

 

[Bradracer18]

yes...the wording I am not real good at, as I didn't know how to word it(you definitely aren't being difficult...I am...as I don't understand this stuff real well...)

In my mind...both the point on the y-axis and the point on the x axis...they are both pointing in the positive z direction...but I might be wrong. Then, those 2 combined would still point in the pos z direction...only at a different angle...??...I don't know...this is a little too confusing for me...ha.

 

[nrqed]

yes...the wording I am not real good at, as I didn't know how to word it(you definitely aren't being difficult...I am...as I don't understand this stuff real well...)

In my mind...both the point on the y-axis and the point on the x

You mean lines of charge along x an dy (those are not points but lines of charge)

axis...they are both pointing in the positive z direction...but I might be wrong. Then, those 2 combined would still point in the pos z direction...only at a different angle...??...I don't know...this is a little too confusing for me...ha.

Yes, the E field vector of each line of charge points in the positive z direction. Now, if two vectors point in the same direction, what can you say about their vector sum?

Patrick

 

[Bradracer18]

Well when you add vectors, don't you find your vectors(2 in the positive z direction)...and then put the tail to the point...which in my head would make the sum be parallel to the xy plane...right?

 

[arunbg]

*Rereads question*
The vector is not parallel to the xy plane, it is perpendicular, or more precisely it is along the +ve z axis . Can you see this ?