What direction should the electric field point in a velocity selector?

[cdymdcool]

A velocity selector consists of a charged particle passing through crossed electirc magnetic fields. The forces exerted by these fields are in opposite directions, and only particles of a certain velocity will move in a straight line. In the following, disregard the magnitudes of the fields. In a velocity selector, the particles move toward the east and the magnetic field is directed to the north. What direction should the electric field point?

Use the right hand rule the B-field force is into the page, so the elctric field force should be out of page. But we don't know the particle's charge how do we determine the direction of the electric field then?

 

[Doc Al]

Use the right hand rule the B-field force is into the page, so the elctric field force should be out of page. But we don't know the particle's charge how do we determine the direction of the electric field then?

Since you don't know the charge, how did you determine the direction of the magnetic force?

Hint: Solve it for positive particles then for negative particles. Compare the two solutions.

 

[cdymdcool]

So the B-field Force is going out of the page, the electric field should be the opposite, going into the page. If particle is positive or negative, the electric field point will both going into the page? But the answer key says down, is it from different perspective?

 

[Doc Al]

To avoid ambiguity, let's use the y-axis for North and the x-axis for East. Assuming East and North (the x-y plane) are parallel to the ground (like usual, on the earth), then the +z-axis would be up. (If your paper is the x-y plane, then the +z-axis would be out of the page.)

So the B-field Force is going out of the page, the electric field should be the opposite, going into the page.

My point was that you cannot know the direction of the magnetic force, since it depends on the sign of the charge. But it doesn't matter! If the particle was positive, then the magnetic force would be in the +z direction and the electric field must point in the -z direction.

If particle is positive or negative, the electric field point will both going into the page?

Figure out what direction the electric field must point if the charge is negative.

But the answer key says down, is it from different perspective?

It looks like they are taking East and North as parallel to the ground, not in the plane of the paper. (See my comments above.)