No Net Force in E & B Perpendicular Fields

[jesuslovesu]

Homework Statement

In a velocity selector E and B fields are perpendicular. Which of the following conditions on the direction of the particle's velocity can result in no net force assuming the E and B are nonzero?

Homework Equations

F = Eq + q(vxB)

The Attempt at a Solution

The answer is B.

A) v is parallel to E
--Not sure why this wouldn't work. Since E is perpendicular to B why can't it result in F = 0? F = E + vB

B) v is parallel to (ExB)
--If I recall my cross product information correctly. v will be perpendicular to both E and B therefore I get F = E + vB.

What's the difference between the two?

 

[G01]

Since the fields are non-zero, the only way for there to be no net force is for the electric and magnetic forces to cancel out (i.e. qv X B is pointing in the opposite direction to qE, and is equal in strength.). Thus, you want the velocity to point in a direction that causes the magnetic force to point opposite the electric force.

Say the electric field points up, and the magnetic field points toward you, using the right hand rule, which way will the velocity have to point in order to get (qv X B) to point opposite qE? This is essentially what the question is asking. If you check the two situations above with the right-hand rule, you should see that only one has qvXB pointing opposite to qE. Can you now see why only one of the above situations work?

 

[Doc Al]

A) v is parallel to E
--Not sure why this wouldn't work. Since E is perpendicular to B why can't it result in F = 0? F = E + vB

If v is parallel to E, what direction will the force from E act? And what direction must q(vxB) act? Can they possibly cancel?

B) v is parallel to (ExB)
--If I recall my cross product information correctly. v will be perpendicular to both E and B therefore I get F = E + vB.

Do the same analysis as before. Compare the directions of qE and q(vxB). Can they cancel?

G01 is way ahead of me. :-)

 

[jesuslovesu]

Understood, thanks