Direction of the torque of the electric force

[november1992]

Homework Statement

http://i.imgur.com/YMuGM.png

Homework Equations

\tau = F * r

The Attempt at a Solution

I don't know how to do these types of problems. My professor didn't even go over this. He just said to use that formula to find the answer.

I know the electric field multiplied by charge is equal to force. In one of the problems the field is pointing downwards and the charge is negative. So I assumed a negative charge multiplied by a field pointing in the negative y direction would result in a force pointing in the positive y direction. That's all I can come up with.

 

[spaderdabomb]

I wouldn't be concerned with which direction the Electric Field is pointing. Electric Fields are almost always drawn as if they are coming from a positive charge, so think of them as positive (repelling a positive point charge, attracting a negative point charge).

So, this specific Electric field is acting on a positive point charge. Since the Electric Field is pointing in the -y direction, there will be a force in the -y direction (there will not be a force in any other direction). However, the Torque will be in a different direction since it's attached to this rod.

This is where r x F comes in. I don't know if your professor taught you this but r x F is pronounced (r cross F), and is called the cross product. r x F = rFsinθ. I don't want to get into too much math though, since that's not what the question asks. It simply asks the direction. The easiest way to do this is something called "The Right Hand Rule." Whenever you have a cross product, point your fingers in the direction of the radius (radius of the rod), then curl your fingers towards the force. Now, whichever way your thumb is pointing is the direction of the torque. In this example, it's pointing "out of the paper" or "out of the computer screen", towards you in the "z" direction.

Hope that helps.

 

[november1992]

So, one of my fingers points downwards, but I don't know the direction of the radius.

 

[november1992]

Well for my thumb to point outward, the radius should be pointing to the left, but why is it pointing to the left and not towards the right?

 

[spaderdabomb]

Because your point your fingers away from the origin of the rod. If you were to place a coordinate system at the base of the rod, the origin would match up with the base of the rod (opposite end of where the charge is). The reason you do this is because the charge is like a pendulum, swinging around the stationary point at the base of the rod.

So point away from the origin, in the direction of the charge.

 

[spaderdabomb]

Sorry if I didn't clarify earlier.

For the negatively charged particle the force is up. For the positively charged particle the force is down. So for the negative charge, your thumb points "into the page" and for the positively charged particle, your thumb points "out of the page".