Magnetic Field and Electric Field Ranking Task

[jcfor3ver]

Homework Statement

First of all, the image for this problem is in an attachment (Jpeg), if you cannot view it let me know and I can change the format.

A positively charged particle moves through a region with uniform electric field pointing toward the top of the page and a uniform magnetic field pointing into the page. The particle can have one of the four velocities shown (initial speed is the same for all). Rank the four possibilities in order of increasing magnitude of the work (W1,W2,and W3) that the system would have to do on the particle to increase its speed by delta v (velocity final- velocity initial). Indicate ties where appropriate.

Homework Equations

F=qv+Bsintheta

Work=Force*distance

Right hand rule to determine direction of Force (if you do not know this, here's a link: http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm )

The Attempt at a Solution

Here is my solution:

For v1: Force due to B and E field is in the positive y direction. Therefore to increase its speed by delta v would require the least amount of work. (since positive particle wants to move in direction of E field, a force due to the B-field in the same direction as the E field would require the least work?)


For v2: The force due to the B-field is perpendicular to the E-field, therefore the work required to cause the particle to speed up is equal to v4 (both are perpendicular to E)

For v3: The force due to B is opposite of the E-field, therefore my intuitive thought is that both forces are pushing against each other, resulting in the most Work that would have to be done by the system in order to increase the particles speed by delta v.

For v4: Same reasoning as v2.


Now those are my thoughts, I just am still confused on if my thinking is correct? My order would therefore be W3>W2=W4>W1

 

[berkeman]

Homework Statement

First of all, the image for this problem is in an attachment (Jpeg), if you cannot view it let me know and I can change the format.

A positively charged particle moves through a region with uniform electric field pointing toward the top of the page and a uniform magnetic field pointing into the page. The particle can have one of the four velocities shown (initial speed is the same for all). Rank the four possibilities in order of increasing magnitude of the work (W1,W2,and W3) that the system would have to do on the particle to increase its speed by delta v (velocity final- velocity initial). Indicate ties where appropriate.

Homework Equations

F=qv+Bsintheta

Work=Force*distance

Right hand rule to determine direction of Force (if you do not know this, here's a link: http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm )

The Attempt at a Solution

Here is my solution:

For v1: Force due to B and E field is in the positive y direction. Therefore to increase its speed by delta v would require the least amount of work. (since positive particle wants to move in direction of E field, a force due to the B-field in the same direction as the E field would require the least work?)


For v2: The force due to the B-field is perpendicular to the E-field, therefore the work required to cause the particle to speed up is equal to v4 (both are perpendicular to E)

For v3: The force due to B is opposite of the E-field, therefore my intuitive thought is that both forces are pushing against each other, resulting in the most Work that would have to be done by the system in order to increase the particles speed by delta v.

For v4: Same reasoning as v2.


Now those are my thoughts, I just am still confused on if my thinking is correct? My order would therefore be W3>W2=W4>W1

The problem is a bit confusing, so I think that's probably the reason nobody has tried to chime in. The question about how much work the system has to do on the particle to increase its velocity by delta-v seems very ill-defined. If you can modulate the E field with time, that changes things significatly. And increase the velocity over how much time? Over what fraction of an orbit, or how many orbits?

But given the problem statement, I think you are probably close to the right answer. However, I'm not sure the middle two are a tie, because as the particle's orbit continues from its current position (and velocity vector directions), one particle turns in the direction of E, and the other turns against it. Again, this goes to whether the problem is asking about an instantaneous amount of work for an instantaneous delta-v, or if they are asking over some portion of the initial orbit.

Hope that helps.