Combined magnetic fields question

s3a

Mar 2009
129
0
Question (with solution): http://i.imgur.com/ZJoSa.jpg

Let x,y be the axes on the sheet of paper where up and right are positive (like the question says actually). I do not get how the use of the right hand-rule should "convince me" that the field of each wire should cancel out in the first and third quadrants.

The way I imagine this is: for the vertical wire, the thumb points in the direction of the current and the fingers point to the negative x direction whereas for the horizontal wire, I imagine the right-hand as having the thumb again in the direction of that current and the fingers in the positive y direction. I really cannot see how this cancels anything out. Am I misusing the right-hand rule or am I just not seeing what it's telling me?

Any help "seeing the light" would be greatly appreciated!
Thanks in advance!
 

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topsquark

Forum Staff
Apr 2008
3,106
659
On the dance floor, baby!
Question (with solution): http://i.imgur.com/ZJoSa.jpg

Let x,y be the axes on the sheet of paper where up and right are positive (like the question says actually). I do not get how the use of the right hand-rule should "convince me" that the field of each wire should cancel out in the first and third quadrants.

The way I imagine this is: for the vertical wire, the thumb points in the direction of the current and the fingers point to the negative x direction whereas for the horizontal wire, I imagine the right-hand as having the thumb again in the direction of that current and the fingers in the positive y direction. I really cannot see how this cancels anything out. Am I misusing the right-hand rule or am I just not seeing what it's telling me?

Any help "seeing the light" would be greatly appreciated!
Thanks in advance!
Since we are dealing with wires I'd use the wire form of the right hand rule: Thumb in the direction of the current and fingers curled in the direction of the magnetic field. It should be easy to see that the field due to the x axis wire is in what would be the direction of the positive z axis, whereas the field due to the y axis wire is in the negative z. (In the first quadrant.)

-Dan
 

s3a

Mar 2009
129
0
Actually, I don't find it easy to see. :(. What I haven't been doing up until now is curling my fingers around the axis which is each respective current direction however, using that logic I feel that both magnetic fields point toward positive z. Also, when they say first and third quadrant, is it actually the first and third quadrant in the xy plane or is it like that just in the drawing since it's impossible to draw 3D images on paper since paper is a 2D surface?
 

topsquark

Forum Staff
Apr 2008
3,106
659
On the dance floor, baby!
Actually, I don't find it easy to see. :(. What I haven't been doing up until now is curling my fingers around the axis which is each respective current direction however, using that logic I feel that both magnetic fields point toward positive z. Also, when they say first and third quadrant, is it actually the first and third quadrant in the xy plane or is it like that just in the drawing since it's impossible to draw 3D images on paper since paper is a 2D surface?
Visualization does get kind of complicated, doesn't it?

In the first quadrant the right hand rule for the current on the +x axis has the fingers curling up out of the paper. That's the +z axis. The wire on the +y has the fingers curling into the page. That's the -z axis.

In the third quadrant the two directions are reversed.

-Dan
 

s3a

Mar 2009
129
0
While I do understand everything you're saying I don't know why the right-hand on the y direction has the fingers curling toward negative z.

Could you please explain that?
 

topsquark

Forum Staff
Apr 2008
3,106
659
On the dance floor, baby!
While I do understand everything you're saying I don't know why the right-hand on the y direction has the fingers curling toward negative z.

Could you please explain that?
I don't know if you've tried this, but clear off a space on your desk. Now take your right hand and place your thumb in the "upward" direction and note that your fingers are pointing into the desk. (It's a tad uncomfortable. sorry about that.) Into the table is the - z direction.

-Dan
 

s3a

Mar 2009
129
0
Sorry if I am annoying you but I'm still confused :(.

When you say "upward direction", I assume you mean positive y (assuming the xy plane is the plane of the sheet of paper) such that the fingers are 90 degrees away from the thumb.

Again, though, I get the "mechanics" of the right-hand rule and the coordinate system. What I am asking about is using theory to know how to position my right-hand.


For example:
In those problems where an electron is undergoing centripetal motion due to a magnetic field, I know that the palm of the hand is to face the centre of the imaginary circle and that the thumb is in direction opposite the velocity of the electron (opposite since the rule is for positive charges) therefore the fingers say that the field is 90 degrees below the thumb.

What I'm having trouble with is proving to myself using theory why the palm is facing negative z instead of positive z for the positive y current for example. In fact, I cannot prove that positive z is correct either. I'm just stuck between the two choices and don't know how to narrow it down to one.

I guess it doesn't matter because either way the fingers are following the same angular path but something matters here and I can't figure out what it is. If I'm unclear about anything in this post, I think it would be better for me to clarify instead of you trying to think what I'm thinking so just tell me.
 

topsquark

Forum Staff
Apr 2008
3,106
659
On the dance floor, baby!
Sorry if I am annoying you but I'm still confused :(.

When you say "upward direction", I assume you mean positive y (assuming the xy plane is the plane of the sheet of paper) such that the fingers are 90 degrees away from the thumb.

Again, though, I get the "mechanics" of the right-hand rule and the coordinate system. What I am asking about is using theory to know how to position my right-hand.


For example:
In those problems where an electron is undergoing centripetal motion due to a magnetic field, I know that the palm of the hand is to face the centre of the imaginary circle and that the thumb is in direction opposite the velocity of the electron (opposite since the rule is for positive charges) therefore the fingers say that the field is 90 degrees below the thumb.

What I'm having trouble with is proving to myself using theory why the palm is facing negative z instead of positive z for the positive y current for example. In fact, I cannot prove that positive z is correct either. I'm just stuck between the two choices and don't know how to narrow it down to one.

I guess it doesn't matter because either way the fingers are following the same angular path but something matters here and I can't figure out what it is. If I'm unclear about anything in this post, I think it would be better for me to clarify instead of you trying to think what I'm thinking so just tell me.
Ah, I see the problem. You can't use that particular right hand rule in this situation. This will explain the rule I have been talking about. Look under the heading "Direction associated with a rotation."

-Dan
 

s3a

Mar 2009
129
0
Actually, I was using that. But, I figured it out! Here is what I did (if anyone else is interested):

The following says which direction the magnetic field is in each quadrant:

For the horizontal wire:
Quadrant 1: up
Quadrant 2: up
Quadrant 3: down
Quadrant 4: down

For the vertical wire:
Quadrant 1: down
Quadrant 2: up
Quadrant 3: up
Quadrant 4: down

I then noticed that it is in quadrants 1 and 3 that each wire has the field in the opposite direction so I know because of that that the magnetic fields cancel in the specified quadrants but to justify that it's that exact line, I thought about the fact that the magnitude of the magnetic field decreases as the distance increases therefore, they only cancel completely at the line y = x.

Solved! Yay! Thanks for your help!
 

topsquark

Forum Staff
Apr 2008
3,106
659
On the dance floor, baby!
Actually, I was using that. But, I figured it out! Here is what I did (if anyone else is interested):

The following says which direction the magnetic field is in each quadrant:

For the horizontal wire:
Quadrant 1: up
Quadrant 2: up
Quadrant 3: down
Quadrant 4: down

For the vertical wire:
Quadrant 1: down
Quadrant 2: up
Quadrant 3: up
Quadrant 4: down

I then noticed that it is in quadrants 1 and 3 that each wire has the field in the opposite direction so I know because of that that the magnetic fields cancel in the specified quadrants but to justify that it's that exact line, I thought about the fact that the magnitude of the magnetic field decreases as the distance increases therefore, they only cancel completely at the line y = x.

Solved! Yay! Thanks for your help!
Good, so long as 'up" and "down" represent the +z and -z axes respectively.

Good job.

-Dan