# Right Hand Rule and Magnetism

#### yan500

Joined Jul 12, 2011
48
Hey all, I've got a question on magnetism and the right hand rule.

A question in my workbook is as follows:

A charge of 2 x 10^-6 C is moving with a velocity of 3 x 10^4 m/s at an angle of 30 degrees with a magnetic field of 0.68 T. What is the direction of the force?

Now, I set it up in an XY coordinate system with B (magnetic field) being on the X axis and V (velocity vector) being 30 degrees above the X axis. If you apply the right hand rule to this you get the answer being into the page. This answer is wrong. The right answer is out of the page. Obviously they set it up with V being on the X axis and B being 30 degrees above. Why did they do it this way and not the way I did it?

I realize I am wrong but I would like to know how to set up a problem like this so next time I wouldn't get it wrong.

Thanks guys!

#### steveb

Joined Jul 3, 2008
2,436
Hey all, I've got a question on magnetism and the right hand rule.

A question in my workbook is as follows:

A charge of 2 x 10^-6 C is moving with a velocity of 3 x 10^4 m/s at an angle of 30 degrees with a magnetic field of 0.68 T. What is the direction of the force?

Now, I set it up in an XY coordinate system with B (magnetic field) being on the X axis and V (velocity vector) being 30 degrees above the X axis. If you apply the right hand rule to this you get the answer being into the page. This answer is wrong. The right answer is out of the page. Obviously they set it up with V being on the X axis and B being 30 degrees above. Why did they do it this way and not the way I did it?

I realize I am wrong but I would like to know how to set up a problem like this so next time I wouldn't get it wrong.

Thanks guys!
You aren't wrong. The question does not set up a coordinate reference frame for you and so you are free to choose your own. Actually, the wording of the problem would have led me to do exactly what you did, because this is the standard mathematical convention. Angle is typically measured counterclockwise off of the x-axis, and that's exactly what you did.

• yan500

#### mik3

Joined Feb 4, 2008
4,843
Just a reminder of the right hand rule:

http://en.wikipedia.org/wiki/Right-hand_rule

The force is pointed at the direction the charge moves.

I think you have confused the force finger (middle) with the current finger (thumb).

• yan500

#### yan500

Joined Jul 12, 2011
48
steveb: Thanks! This was a problem from Schaum's Outlines so I guess the book is not as great as everyone says it is haha.

mik3: There is no current in this problem. Using the finger method for the right hand rule in this context designates your index finger as the velocity, middle finger as B (magnetic field) and your thumb points in the direction of the force. I used this method and still got the "wrong" answer. Thanks for your response!

#### mik3

Joined Feb 4, 2008
4,843
steveb: Thanks! This was a problem from Schaum's Outlines so I guess the book is not as great as everyone says it is haha.

mik3: There is no current in this problem. Using the finger method for the right hand rule in this context designates your index finger as the velocity, middle finger as B (magnetic field) and your thumb points in the direction of the force. I used this method and still got the "wrong" answer. Thanks for your response!
There is I in the direction of the velocity!

#### yan500

Joined Jul 12, 2011
48
Hmm...So why does the answer change when they ask you the same question, only this time the velocity is at an angle of 150 degrees? The right answer then is into the page. Wouldn't it still be out of the page?

#### mik3

Joined Feb 4, 2008
4,843
Hmm...So why does the answer change when they ask you the same question, only this time the velocity is at an angle of 150 degrees? The right answer then is into the page. Wouldn't it still be out of the page?
It depends where is the reference side of the angle.

Can you provide a diagram?

#### yan500

Joined Jul 12, 2011
48
They give no diagram and give no reference. All the information they give I have listed. That's why I'm so confused haha. In other problems that they ask you to solve they give a diagram and I got all those problems right, but this one they seem to have arbitrarily chosen reference sides.

#### mik3

Joined Feb 4, 2008
4,843
They give no diagram and give no reference. All the information they give I have listed. That's why I'm so confused haha. In other problems that they ask you to solve they give a diagram and I got all those problems right, but this one they seem to have arbitrarily chosen reference sides.
How do they measure the angle usually?

With reference to a parallel line to the B or to a perpendicular line to B.

#### mik3

Joined Feb 4, 2008
4,843
The crazy thing is the answer is not even drawn on an axis.

It would look like this: They would show that picture and then explain why the answer was out of the page, but they wouldn't explain why they set the vectors up the way that they did.
If it is like this, then at 30 the charge moves in the same direction as B. At 150 the charge moves in the opposite direction, thus the force direction changes.

#### yan500

Joined Jul 12, 2011
48
Can you elaborate on that? I'm having difficulty understanding.

#### mik3

Joined Feb 4, 2008
4,843
Can you elaborate on that? I'm having difficulty understanding.
Rotate V by 150 degrees.

Where does it point to?

#### yan500

Joined Jul 12, 2011
48
Oh alright I see. But could you technically set it up the way I did? Would the answer still be right since they did not define a reference axis? I would get the opposite answer to both questions, so one would be into the page and the other out.

#### steveb

Joined Jul 3, 2008
2,436
Oh alright I see. But could you technically set it up the way I did? Would the answer still be right since they did not define a reference axis? I would get the opposite answer to both questions, so one would be into the page and the other out.
Yes, the setup of the problem is arbitrary, but once you chose the setup, then the fact that the direction changes for a 180 degree change in one of the vectors, is not arbitrary. The change in direction of either vector introduces a minus sign into the cross product. The minus sign in the force simply means that the force is in the other direction.

The bottom line is that the wording of the problem is too vague to give the answer in terms of whether it is in/out of the page. You need to identify which vector is rotated clockwise relative to the other, to answer that. In determining which vector is clockwise relative to the other, you always use the smallest possible angle. (for example 90 deg and not 270 deg)